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Reciprocal Distance Laplacian Eigenvalue Distribution Based on Graph Parameters
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作者 CUI Jiaxin MA Xiaoling 《新疆大学学报(自然科学版中英文)》 CAS 2024年第5期562-570,共9页
Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I ... Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices. 展开更多
关键词 reciprocal distance Laplacian eigenvalue VERTEX-CONNECTIVITY independence number pendant vertices
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Asymptotic upper bounds for wheel:complete graph Ramsey numbers
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作者 宋洪雪 《Journal of Southeast University(English Edition)》 EI CAS 2004年第1期126-129,共4页
It is shown that r(W_m, K_n)≤(1+o(1))C_1n log n 2m-2m-2 for fixed even m≥4 and n→∞, and r(W_m, K_n)≤(1+o(1))C_2n 2mm+1 log n m+1m-1 for fixed odd m≥5 and n→∞, wher... It is shown that r(W_m, K_n)≤(1+o(1))C_1n log n 2m-2m-2 for fixed even m≥4 and n→∞, and r(W_m, K_n)≤(1+o(1))C_2n 2mm+1 log n m+1m-1 for fixed odd m≥5 and n→∞, where C_1=C_1(m)>0 and C_2=C_2(m)>0, in particular, C_2=12 if m=5 . It is obtained by the analytic method and using the function f_m(x)=∫ 1 _ 0 (1-t) 1m dtm+(x-m)t , x≥0 , m≥1 on the base of the asymptotic upper bounds for r(C_m, K_n) which were given by Caro, et al. Also, cn log n 52 ≤r(K_4, K_n)≤(1+o(1)) n 3 ( log n) 2 (as n→∞ ). Moreover, we give r(K_k+C_m, K_n)≤(1+o(1))C_5(m)n log n k+mm-2 for fixed even m≥4 and r(K_k+C_m, K_n)≤(1+o(1))C_6(m)n 2+(k+1)(m-1)2+k(m-1) log n k+2m-1 for fixed odd m≥3 (as n→∞ ). 展开更多
关键词 Ramsey numbers WHEELS independent number complete graphs
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SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION
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作者 潘娟 周云华 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1382-1402,共21页
We consider the style number, independence number and entropy for a frame bundle dynamical system. The base system of which is a countable discrete amenable group action on a compact metric space. We obtain the existe... We consider the style number, independence number and entropy for a frame bundle dynamical system. The base system of which is a countable discrete amenable group action on a compact metric space. We obtain the existence of cover measures, an ergodic theorem about mean linear independence and the style number, and a variational principle for style numbers and independence numbers. We also study the relationship between the entropy of base systems and that of their bundle systems. 展开更多
关键词 mean linear independence style number independence number ENTROPY
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A POLYNOMIAL ALGORITHM FOR FINDING THEMINIMUM FEEDBACK VERTEX SET OF A3-REGULAR SIMPLE GRAPH 被引量:2
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作者 李德明 刘彦佩 《Acta Mathematica Scientia》 SCIE CSCD 1999年第4期375-381,共7页
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert... A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided. 展开更多
关键词 maximum genus nonseparating independent number feedback vertex set 3-regular graph adjacency matching
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Neighbourhood Conditions and Hamiltonian Properties
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作者 杨治辉 《Journal of Southeast University(English Edition)》 EI CAS 1998年第2期121-123,共3页
This paper gives new sufficient conditions for a connected graph to be Hamiltonian and Hamiltonian connected by independence number and neighbourhood intersections of three independent vertices with distance 2.
关键词 neighbourhood Hamilton cycle/path independence number
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ON k-DIAMETER OF k-CONNECTED GRAPHS
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作者 Xu Junming Xu Keli of Math., Univ. of Science and Technology of China, Hefei 230026. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第3期231-236,共6页
Let G be a k-connected simple graph with order n. The k-diameter, combining connectivity with diameter, of G is the minimum integer d k(G) for which between any two vertices in G there are at least k internally verte... Let G be a k-connected simple graph with order n. The k-diameter, combining connectivity with diameter, of G is the minimum integer d k(G) for which between any two vertices in G there are at least k internally vertex-disjoint paths of length at most d k(G). For a fixed positive integer d, some conditions to insure d k(G)≤d are given in this paper. In particular, if d≥3 and the sum of degrees of any s (s =2 or 3) nonadjacent vertices is at least n+(s-1)k+1-d, then d k(G)≤d. Furthermore, these conditions are sharp and the upper bound d of k-diameter is best possible. 展开更多
关键词 DIAMETER k-diameter CONNECTIVITY independence number fault-tolerant networks.
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RELATIONS AMONG SOME PARAMETERS OF HYPERGRAPHS
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作者 Sun Haina Bu Yuehua 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第4期487-492,共6页
The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows:Dv(H)≤min{α≤(H), p(H), p(H), T(H)}; De(H)≤min{v(H), T... The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows:Dv(H)≤min{α≤(H), p(H), p(H), T(H)}; De(H)≤min{v(H), T(H), p(H)}; DT(H) ≤αT(H); S(H)≤ Dv (H) + α(H)≤n; 2≤ Dv (H) + T(H) ≤n; 2 〈 Dv (H) + v(H)≤n/2 + [n/r]; Dv (H) + p(H) 〈_n;2≤De(H) + Dv(H)≤n/2 + [n/r];α(H) + De(H)≤n;2 ≤ De(H) + v(H)≤2[n/r]; 2 De(H) + p(H)≤n-r + 2. 展开更多
关键词 HYPERGRAPHS dominating number independence number covering number
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The Independence-Separation Problem on the 3-D Rook’s Graph
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作者 Paul A. Burchett 《Open Journal of Discrete Mathematics》 2016年第3期167-173,共7页
Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem... Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added. 展开更多
关键词 CHESS Independence-Separation number Independence number p-Dimensional Grid-Line Graphs p-Dimensional Rook’s Graph
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A Method for the Solution of the 2D-Oswatitsch Equations
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作者 Volkmar Lorenz Christian Mundt 《Journal of Applied Mathematics and Physics》 2016年第4期844-856,共13页
Corresponding to Oswatitsch’s Mach number independence principle the Mach number of hypersonic inviscid flows, , does not affect components of various non-dimensional formulations such as velocity and density, pressu... Corresponding to Oswatitsch’s Mach number independence principle the Mach number of hypersonic inviscid flows, , does not affect components of various non-dimensional formulations such as velocity and density, pressure coefficients and Mach number behind a strong shock. On this account, the principle is significant in the development process for hypersonic vehicles. Oswatitsch deduced a system of partial differential equations which describes hypersonic flow. These equations are the basic gasdynamic equations as well as Crocco’s theorem which are reduced for the case of very high Mach numbers, . Their numerical solution can not only result in simplified algorithms prospectively utilized to describe the flow around bodies flying mainly in the lower stratosphere with very high Mach numbers. It also offers a deeper understanding of similarity effects for hypersonic flows. In this paper, a solution method for Oswatisch’s equations for perfect gas, based on a 4-step Runge-Kutta-algorithm, is presented including a fast shock-fitting procedure. An analysis of numerical stability is followed by a detailed comparison of results for different Mach numbers and ratios of the specific heats. 展开更多
关键词 Oswatitsch Mach number Independence Bow Shock PDE Time Dependent Solution Ratios of Specific Heats
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Sharp Bounds on the A_(α)-index of Graphs in Terms of the Independence Number
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作者 Wan-ting SUN Li-xia YAN +1 位作者 Shu-chao LI Xue-chao LI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2023年第3期656-674,共19页
Given a graph G,the adjacency matrix and degree diagonal matrix of G are denoted by A(G)and D(G),respectively.In 2017,Nikiforov~([24])proposed the A_(α)-matrix:A_α(G)=αD(G)+(1-α)A(G),whereα∈[0,1].The largest eig... Given a graph G,the adjacency matrix and degree diagonal matrix of G are denoted by A(G)and D(G),respectively.In 2017,Nikiforov~([24])proposed the A_(α)-matrix:A_α(G)=αD(G)+(1-α)A(G),whereα∈[0,1].The largest eigenvalue of this novel matrix is called the A_(α)-index of G.In this paper,we characterize the graphs with minimum A_(α)-index among n-vertex graphs with independence number i forα∈[0,1),where i=1,[n/2],[n/2],[n/2]+1,n-3,n-2,n-1,whereas for i=2 we consider the same problem forα∈[0,3/4].Furthermore,we determine the unique graph(resp.tree)on n vertices with given independence number having the maximum A_(α)-index withα∈[0,1),whereas for the n-vertex bipartite graphs with given independence number,we characterize the unique graph having the maximum A_α-index withα∈[1/2,1). 展开更多
关键词 independence number spectral radius A_(α)-index bipartite graph
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Independent Roman{2}-Domination in Trees
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作者 LI Bei-bei SHANG Wei-ping 《Chinese Quarterly Journal of Mathematics》 2022年第4期386-393,共8页
For a graph G=(V,E),a Roman{2}-dominating function f:V→{0,1,2}has the property that for every vertex v∈V with f(v)=0,either v is adjacent to at least one vertex u for which f(u)=2,or at least two vertices u1 and u2 ... For a graph G=(V,E),a Roman{2}-dominating function f:V→{0,1,2}has the property that for every vertex v∈V with f(v)=0,either v is adjacent to at least one vertex u for which f(u)=2,or at least two vertices u1 and u2 for which f(u1)=f(u2)=1.A Roman{2}-dominating function f=(V0,V1,V2)is called independent if V1∪V2 is an independent set.The weight of an independent Roman{2}-dominating function f is the valueω(f)=Σv∈V f(v),and the independent Roman{2}-domination number i{R2}(G)is the minimum weight of an independent Roman{2}-dominating function on G.In this paper,we characterize all trees with i{R2}(T)=γ(T)+1,and give a linear time algorithm to compute the value of i{R2}(T)for any tree T. 展开更多
关键词 Domination number Roman{2}-dominating function Independent Roman{2}-domination number
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MAXIMUM GENUS,INDEPENDENCE NUMBER AND GIRTH 被引量:8
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作者 HUANGYUANQIU LIUYANPEI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2000年第1期77-82,共6页
It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of th... It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of the independence number as well as the girth of a graph, and thus use the formulation in [2] to translate this result to lower bound on the maximum genus. Meantime it is shown that both of the bounds are best possible. 展开更多
关键词 Maximum genus Betti deficiency Independence number GIRTH
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Upper embeddability,edge independence number and girth 被引量:2
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作者 OUYANG ZhangDong TANG Ling HUANG YuanQiu 《Science China Mathematics》 SCIE 2009年第9期1939-1946,共8页
Combined with the edge-connectivity, this paper investigates the relationship between the edge independence number and upper embeddability. And we obtain the following result:Let G be a k-edge-connected graph with gir... Combined with the edge-connectivity, this paper investigates the relationship between the edge independence number and upper embeddability. And we obtain the following result:Let G be a k-edge-connected graph with girth g. If $$ \alpha '(G) \leqslant ((k - 2)^2 + 2)\left\lfloor {\frac{g} {2}} \right\rfloor + \frac{{1 - ( - 1)^g }} {2}((k - 1)(k - 2) + 1) - 1, $$ where k = 1, 2, 3, and α′(G) denotes the edge independence number of G, then G is upper embeddable and the upper bound is best possible. And it has generalized the relative results. 展开更多
关键词 GRAPH upper embeddability edge independence number GIRTH 05C10
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Strong laws of large numbers for sub-linear expectations 被引量:26
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作者 CHEN ZengJing 《Science China Mathematics》 SCIE CSCD 2016年第5期945-954,共10页
We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out... We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities. 展开更多
关键词 capacity strong law of large numbers independently and identically distributed nonlinear expectation
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Conflict-free Connection Number and Independence Number of a Graph 被引量:1
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作者 Jing WANG Meng JI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2021年第2期278-286,共9页
An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path,which contains a color used on exactly one of its edges.The conflict-free connection number of a connected graph G,... An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path,which contains a color used on exactly one of its edges.The conflict-free connection number of a connected graph G,denoted by cf c(G),is defined as the minimum number of colors that are required in order to make G conflict-free connected.In this paper,we investigate the relation between the conflict-free connection number and the independence number of a graph.We firstly show that cf c(G)≤α(G)for any connected graph G,and give an example to show that the bound is sharp.With this result,we prove that if T is a tree with?(T)≥(α(T)+2)/2,then cf c(T)=?(T). 展开更多
关键词 EDGE-COLORING conflict-free connection number independence number TREE
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The lower bound on independence number
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作者 李雨生 CecilC.ROUSSEAU 臧文安 《Science China Mathematics》 SCIE 2002年第1期64-69,共6页
Let G be a graph with degree sequence ( dv). If the maximum degree of any subgraph induced by a neighborhood of G is at most m, then the independence number of G is at least $\sum\limits_v {f_{m + 1} \left( {d_v } \ri... Let G be a graph with degree sequence ( dv). If the maximum degree of any subgraph induced by a neighborhood of G is at most m, then the independence number of G is at least $\sum\limits_v {f_{m + 1} \left( {d_v } \right)} $ , where fm+1( x) is a function greater than $\frac{{log\left( {x/\left( {m + 1} \right)} \right) - 1}}{x}for x > 0$ for x> 0. For a weighted graph G = ( V, E, w), we prove that its weighted independence number (the maximum sum of the weights of an independent set in G) is at least $\sum\limits_v {\frac{{w_v }}{{1 + d_v }}} $ where wv is the weight of v. 展开更多
关键词 independence number discrete form weighted graph
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A Note on Algebraic Independence of Numbers
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作者 朱尧辰 《Acta Mathematica Sinica,English Series》 SCIE 1985年第3期251-254,共4页
1.IntroductionWe denote the set of all positive integers by N,and the fields of all rational,algebraic numbers by Q,A,respectively.Let Z~* [Z1,…,Z2] be the set of all non-zero polynomials in variables Z1,…,Z2,with i... 1.IntroductionWe denote the set of all positive integers by N,and the fields of all rational,algebraic numbers by Q,A,respectively.Let Z~* [Z1,…,Z2] be the set of all non-zero polynomials in variables Z1,…,Z2,with integer coefficients.For α∈A we denotemaxand multiply from i=1 to α~((i)) by and N(a),respectively;where d is the degree of α,and 展开更多
关键词 A Note on Algebraic Independence of numbers
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Binding Numbers for Fractional ID-k-factor-critical Graphs
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作者 Si Zhong ZHOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第1期181-186,共6页
LetG be a graph,and k≥2 be a positive integer.A graph G is fractional independentset-deletable k-factor-critical(in short,fractional ID-k-factor-critical),if G I has a fractional k-factor for every independent set ... LetG be a graph,and k≥2 be a positive integer.A graph G is fractional independentset-deletable k-factor-critical(in short,fractional ID-k-factor-critical),if G I has a fractional k-factor for every independent set I of G.The binding number bind(G)of a graph G is defined as bind(G)=min|NG(X)||X|:=X V(G),NG(X)=V(G).In this paper,it is proved that a graph G is fractional ID-k-factor-critical if n≥6k 9 and bind(G)〉(3k 1)(n 1)kn 2k+2. 展开更多
关键词 Graph binding number independent set fractionalk-factor fractional ID-k-factor-criti-cal
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Some Results on Spanning Trees 被引量:8
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作者 Bing Yao Zhong-fu Zhang Jian-fang Wang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2010年第4期607-616,共10页
Some structures of spanning trees with many or less leaves in a connected graph are determined.We show(1) a connected graph G has a spanning tree T with minimum leaves such that T contains a longest path,and(2) a ... Some structures of spanning trees with many or less leaves in a connected graph are determined.We show(1) a connected graph G has a spanning tree T with minimum leaves such that T contains a longest path,and(2) a connected graph G on n vertices contains a spanning tree T with the maximum leaves such that Δ(G) =Δ(T) and the number of leaves of T is not greater than n D(G)+1,where D(G) is the diameter of G. 展开更多
关键词 Spanning tree LEAVES DIAMETER Steiner tree independent number
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Structure of Independent Sets in Direct Products of Some Vertex-transitive Graphs 被引量:1
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作者 Xing Bo GENG Jun WANG Hua Jun ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第4期697-706,共10页
Let Circ(r, n) be a circular graph. It is well known that its independence number α(Circ(r, n)) = r. In this paper we prove that for every vertex transitive graph H, and describe the structure of maximum indepe... Let Circ(r, n) be a circular graph. It is well known that its independence number α(Circ(r, n)) = r. In this paper we prove that for every vertex transitive graph H, and describe the structure of maximum independent sets in Circ(r, n) × H. As consequences, we prove for G being Kneser graphs, and the graphs defined by permutations and partial permutations, respectively. The structure of maximum independent sets in these direct products is also described. 展开更多
关键词 Vertex-transitivity PRIMITIVITY independence number
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