期刊文献+
共找到18篇文章
< 1 >
每页显示 20 50 100
On the ordering of the Kirchhoff indices of the complements of trees and unicyclic graphs 被引量:1
1
作者 CHEN Xiao-dan HAO Guo-liang JIN De-quan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2020年第3期308-320,共13页
The Kirchhoff index Kf(G) of a graph G is defined to be the sum of the resistance distances between all pairs of vertices of G. In this paper, we develop a novel method for ordering the Kirchhoff indices of the comple... The Kirchhoff index Kf(G) of a graph G is defined to be the sum of the resistance distances between all pairs of vertices of G. In this paper, we develop a novel method for ordering the Kirchhoff indices of the complements of trees and unicyclic graphs. With this method, we determine the first five maximum values of Kf■ and the first four maximum values of Kf(ū),where ■ and ū are the complements of a tree T and unicyclic graph U, respectively. 展开更多
关键词 Kirchhoff index TREE unicyclic graph COMPLEMENT ORDERING
下载PDF
Unicyclic graphs with extremal Lanzhou index 被引量:1
2
作者 LIU Qian-qian LI Qiu-li ZHANG He-ping 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2022年第3期350-365,共16页
Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its compleme... Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its complement respectively.Lanzhou index Lz(G)can be expressed as(n-1)M_(1)(G)-F(G),where M_(1)(G)and F(G)denote the first Zagreb index and the forgotten index of G respectively,and n is the number of vertices in G.It turns out that Lanzhou index outperforms M_(1)(G)and F(G)in predicting the logarithm of the octanol-water partition coefficient for octane and nonane isomers.It was shown that stars and balanced double stars are the minimal and maximal trees for Lanzhou index respectively.In this paper,we determine the unicyclic graphs and the unicyclic chemical graphs with the minimum and maximum Lanzhou indices separately. 展开更多
关键词 Lanzhou index unicyclic graph extremal graph Zagreb index forgotten index
下载PDF
The lower bound of revised edge-Szeged index of unicyclic graphs with given diameter
3
作者 Min WANG Mengmeng LIU 《Frontiers of Mathematics in China》 CSCD 2023年第4期251-275,共25页
Given a connected graph G,the revised edge-revised Szeged index is defined as Sz_(e)^(*)(G)=∑_(e=uv∈E_(G))(m_(u)(e)+m_(0)(e)/2)(m_(v)(e)+m_(0)(e)/w),where m_(u)(e),m_(v)(e)and m_(0)(e)are the number of edges of G ly... Given a connected graph G,the revised edge-revised Szeged index is defined as Sz_(e)^(*)(G)=∑_(e=uv∈E_(G))(m_(u)(e)+m_(0)(e)/2)(m_(v)(e)+m_(0)(e)/w),where m_(u)(e),m_(v)(e)and m_(0)(e)are the number of edges of G lying closer to vertex u than to vertex u,the number of edges of G lying closer to vertex than to vertex u and the number of edges of G at the same distance to u and u,respectively.In this paper,by transformation and calculation,the lower bound of revised edge-Szeged index of unicyclic graphs with given diameter is obtained,and the extremal graph is depicted. 展开更多
关键词 Wiener index revised edge Szeged index unicyclic graph extremal graph
原文传递
LARGEST EIGENVALUE OF A UNICYCLIC MIXED GRAPH 被引量:4
4
作者 Fan YizhengDept. of Math., Nanjing Normal Univ., Jiangsu 210097,China Dept. of Math., Anhui Univ., Anhui 230039,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第2期140-148,共9页
The graphs which maximize and minimize respectively the largest eigenvalue over all unicyclic mixed graphs U on n vertices are determined. The unicyclic mixed graphs U with the largest eigenvalue λ 1(U)=n or λ 1(U... The graphs which maximize and minimize respectively the largest eigenvalue over all unicyclic mixed graphs U on n vertices are determined. The unicyclic mixed graphs U with the largest eigenvalue λ 1(U)=n or λ 1(U)∈(n,n+1] are characterized. 展开更多
关键词 mixed graph unicyclic graph Laplacian eigenvalue.
下载PDF
Unicyclic Graphs with Nullity One 被引量:4
5
作者 Ke Shi QIAN 《Journal of Mathematical Research and Exposition》 CSCD 2010年第5期825-832,共8页
The nullity of a graph G is defined to be the multiplicity of the eigenvalue zero in its spectrum. In this paper we characterize the unicyclic graphs with nullity one in aspect of its graphical construction.
关键词 nullity of graphs unicyclic graphs SINGULARITY perfectly matched vertex.
下载PDF
The Least Eigenvalue of Unicyclic Graphs with Application to Spectral Spread 被引量:1
6
作者 Jiming Guo Gege Zhang +1 位作者 Zhiwen Wang Panpan Tong 《Algebra Colloquium》 SCIE CSCD 2022年第2期265-272,共8页
Let U^(g)_(n)be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),…,T_(g))∈U^(g)_(n)be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in an anticlockwise direction)by identifying v_(i)with... Let U^(g)_(n)be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),…,T_(g))∈U^(g)_(n)be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in an anticlockwise direction)by identifying v_(i)with the root of a rooted tree T_(i)of order n_(i)for each i=1,2,…,g,where n_(i)≥1 and∑^(g)_(i=1)n_(i)=n.In this note,the graph with the minimal least eigenvalue(and the graph with maximal spread)in C(T_(1),T_(2),…,T_(g))is determined. 展开更多
关键词 adjacency matrix least eigenvalue EIGENVECTOR unicyclic graph
原文传递
A Note on the Nullity of Unicyclic Graphs 被引量:1
7
作者 Wei ZHU Ting Zeng WU Sheng Biao HU 《Journal of Mathematical Research and Exposition》 CSCD 2010年第5期817-824,共8页
The number of zero eigenvalues in the spectrum of the graph G is called its nullity and is denoted by η(G). In this paper, we determine the all extremal unicyclic graphs achieving the fifth upper bound n - 6 and th... The number of zero eigenvalues in the spectrum of the graph G is called its nullity and is denoted by η(G). In this paper, we determine the all extremal unicyclic graphs achieving the fifth upper bound n - 6 and the sixth upperbound n - 7. 展开更多
关键词 EIGENVALUES NULLITY unicyclic graphs.
下载PDF
A Comparison between the Metric Dimension and Zero Forcing Number of Trees and Unicyclic Graphs
8
作者 Linda EROH Cong X.KANG Eunjeong YI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2017年第6期731-747,共17页
The metric dimension dim(G) of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcing number Z(G) of a gr... The metric dimension dim(G) of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcing number Z(G) of a graph G is the minimum eardinality of a set S of black vertices (whereas vertices in V(G)/S are colored white) such that V(G) is turned black after finitely many applications of "the color-change rule": a white vertex is converted black if it is the only white neighbor of a black vertex. We show that dim(T) ≤Z(T) for a tree T, and that dim(G)≤Z(G)+I if G is a unicyclic graph; along the way, we characterize trees T attaining dim(T) = Z(T). For a general graph G, we introduce the "cycle rank conjecture". We conclude with a proof of dim(T) - 2 ≤ dim(T + e) ≤dim(T) + 1 for e∈ E(T). 展开更多
关键词 DISTANCE resolving set metric dimension zero forcing set zero forcing number tree unicyclic graph cycle rank
原文传递
Improved Upper Bounds for the Largest Eigenvalue of Unicyclic Graphs
9
作者 HU Sheng Biao 《Journal of Mathematical Research and Exposition》 CSCD 2009年第5期945-950,共6页
Let G(V, E) be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V(Cm). The G - E(Cm) are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti an... Let G(V, E) be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V(Cm). The G - E(Cm) are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui : i = 1, 2 , m}. Let κ = ec+1. Forj = 1,2,...,k- 1, let δij = max{dv : dist(v, ui) = j,v ∈ Ti}, δj = max{δij : i = 1, 2,..., m}, δ0 = max{dui : ui ∈ V(Cm)}. Then λ1(G)≤max{max 2≤j≤k-2 (√δj-1-1+√δj-1),2+√δ0-2,√δ0-2+√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 (G) is the largest eigenvalue of the adjacency matrix of G. 展开更多
关键词 unicyclic graph adjacency matrix largest eigenvalue.
下载PDF
ON q-WIENER INDEX OF UNICYCLIC GRAPHS
10
作者 Xing Feng Jianping Ou Shaihua Liu 《Annals of Applied Mathematics》 2018年第3期263-268,共6页
The q-Wiener index of unicyclic graphs are determined in this work. As an example of its applications, an explicit expression of q-Wiener index of caterpillar cycles is presented.
关键词 q-Wiener index unicyclic graphs caterpillar cycles
原文传递
On Graphs with Equal Connected Domination and 2-connected Domination Numbers
11
作者 CHEN Hong-yu ZHU Zhe-li 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期98-103,共6页
A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck(G) of G is the minimum cardinality taken ove... A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck(G) of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers. 展开更多
关键词 connected domination number 2-connected domination number trees unicyclic graphs
下载PDF
Research on the Eigenvalues of Graphs and Mixed Graphs
12
作者 Zhihui Ma Huimin Jiang 《International Journal of Technology Management》 2015年第1期109-110,共2页
This paper first elaborates the research situation and progress of Laplace characteristics and the eigenvalues value of graphs. The second is given an upper bound of characteristic value of a kind of special graph usi... This paper first elaborates the research situation and progress of Laplace characteristics and the eigenvalues value of graphs. The second is given an upper bound of characteristic value of a kind of special graph using the properties of similar matrices. At the same time, a new upper bound of Laplace characteristic values are given using properties of Laplace matrix and the similarity matrix, to improve the existing results. Then, we use the example of the upper bound of our results are more precise than some previous results. Finally the use Laplace non- zero eigenvalues of graph properties to give a bound expressions using the degree of square with a number of edges and the graph of the number, number of connected component expression map, it reflected the relationship between eigenvalues and the amount of Laplace. 展开更多
关键词 graph EIGENVALUE Nonsingular unicyclic mixed graph
下载PDF
A Note on Comparison Between the Wiener Index and the Zagreb Indices 被引量:1
13
作者 YOU ZHI-FU HUANG YU-FEI Du Xian-kun 《Communications in Mathematical Research》 CSCD 2018年第4期296-302,共7页
In this note, we correct a wrong result in a paper of Das et al. with regard to the comparison between the Wiener index and the Zagreb indices for trees (Das K C, Jeon H, Trinajstic N. The comparison between the Wie... In this note, we correct a wrong result in a paper of Das et al. with regard to the comparison between the Wiener index and the Zagreb indices for trees (Das K C, Jeon H, Trinajstic N. The comparison between the Wiener index and the Zagreb indices and the eccentric connectivity index for trees. Discrete Appl. Math., 2014, 171:35 41), and give a simple way to compare the Wiener index and the Zagreb indices for trees. Moreover, the comparison between the Wiener index and the Zagreb indices for unicyclic graphs is carried out. 展开更多
关键词 Wiener index Zagreb indice TREE unicyclic graph
下载PDF
BICYCLIC GRAPHS WITH UNICYCLIC OR BICYCLIC INVERSES
14
作者 Xia Wang Hong Bian Haizheng Yu 《Annals of Applied Mathematics》 2020年第3期270-281,共12页
A graph G is nonsingular if its adjacency matrix A(G)is nonsingular.A nonsingular graph G is said to have an inverse G+if A(G)-1 is signature similar to a nonnegative matrix.Let H be the class of connected bipartite g... A graph G is nonsingular if its adjacency matrix A(G)is nonsingular.A nonsingular graph G is said to have an inverse G+if A(G)-1 is signature similar to a nonnegative matrix.Let H be the class of connected bipartite graphs with unique perfect matchings.We present a characterization of bicyclic graphs in H which possess unicyclic or bicyclic inverses. 展开更多
关键词 inverse graph unicyclic graph bicyclic graph perfect matching
原文传递
2-Walk Linear Graphs with Small Number of Cycles 被引量:1
15
作者 FAN Qiong QI Huan 《Wuhan University Journal of Natural Sciences》 CAS 2010年第5期375-379,共5页
A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk(a,b)-linear graph must obey.Using these conditions and some basic the... A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk(a,b)-linear graph must obey.Using these conditions and some basic theorems in graph theory,we characterize all 2-walk linear graphs with small cyclic graphs without pendants.The results are given in sort on unicyclic,bicyclic,tricyclic graphs. 展开更多
关键词 2-walk linear graphs unicyclic graphs bicyclic graphs tricyclic graphs
原文传递
On Strong Metric Dimension of Graphs and Their Complements
16
作者 Eunjeong YI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第8期1479-1492,共14页
A vertex x in a graph G strongly resolves a pair of vertices v, w if there exists a shortest x-w path containing v or a shortest x-v path containing w in G. A set of vertices SV(G) is a strong resolving set of G if ... A vertex x in a graph G strongly resolves a pair of vertices v, w if there exists a shortest x-w path containing v or a shortest x-v path containing w in G. A set of vertices SV(G) is a strong resolving set of G if every pair of distinct vertices of G is strongly resolved by some vertex in S. The strong metric dimension of G, denoted by sdim(G), is the minimum cardinality over all strong resolving sets of G. For a connected graph G of order n≥2, we characterize G such that sdim(G) equals 1, n-1, or n-2, respectively. We give a Nordhaus–Gaddum-type result for the strong metric dimension of a graph and its complement: for a graph G and its complement G, each of order n≥4 and connected, we show that 2≤sdim(G)+sdim(G)≤2( n-2). It is readily seen that sdim(G)+sdim(G)=2 if and only if n=4; we show that, when G is a tree or a unicyclic graph, sdim(G)+sdim(G)=2(n 2) if and only if n=5 and G ~=G ~=C5, the cycle on five vertices. For connected graphs G and G of order n≥5, we show that 3≤sdim(G)+sdim(G)≤2(n-3) if G is a tree; we also show that 4≤sdim(G)+sdim(G)≤2(n-3) if G is a unicyclic graph of order n≥6. Furthermore, we characterize graphs G satisfying sdim(G)+sdim(G)=2(n-3) when G is a tree or a unicyclic graph. 展开更多
关键词 Strong resolving set strong metric dimension Nordhaus–Gaddum-type TREE unicyclic graph
原文传递
Number of Induced Matchings of Graphs
17
作者 Yan CHEN Yan LIU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2021年第1期35-47,共13页
A matching M of a graph G is an induced matching if no two edges in M arejoined by an edge of G.Let iz(G) denote the total number of induced matchings of G,named iz-index.It is well known that the Hosoya index of a gr... A matching M of a graph G is an induced matching if no two edges in M arejoined by an edge of G.Let iz(G) denote the total number of induced matchings of G,named iz-index.It is well known that the Hosoya index of a graph is the total number of matchings and the Hosoya index of a path can be calculated by the Fibonacci sequence.In this paper,we investigate the iz-index of graphs by using the Fibonacci-Narayana sequence and characterize some types of graphs with minimum and maximum iz-index,respectively. 展开更多
关键词 induced matching Fibonacci-Narayana sequence TREE unicyclic graph
原文传递
On the Merrifield-Simmons Indices and Hosoya Indices of Cyclic Graphs
18
作者 Wenting Zheng Hongmei Liu Zhen Yu 《Journal of Systems Science and Information》 2009年第2期111-118,共8页
The Merrifield-Simmons index and Hosoya index are defined as the number of the graph G(V, E) as the number of subsets of V(G) in which no tow vertices are adjacent and the number of subsets of E(G) in which no t... The Merrifield-Simmons index and Hosoya index are defined as the number of the graph G(V, E) as the number of subsets of V(G) in which no tow vertices are adjacent and the number of subsets of E(G) in which no two edges are incident, respectively. In this paper, we characterize the Unicyclic graphs with Merrifield-Simmons indices and Hosoya indices, respectively. And double-cyclic graphs with Hosoya indices among the doublecyclic graphs with n vertices. 展开更多
关键词 Merrifield-Simmons index Hosoya index unicyclic graph double-cyclicgraph grith
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部