Adjacent Vertex-distinguishing E-total Coloring on Some Join Graphs Cm V Gn

Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.

<i>L</i>(2,1)-Labeling Number of the Product and the Join Graph on Two Fans

L(2,1)-labeling number of the product and the join graph on two fans are discussed in this paper, we proved that L(2,1)-labeling number of the product graph on two fans is?λ(G) ≤ Δ+3 , L(2,1)-labeling number of the join graph on two fans is?λ(G) ≤ 2Δ+3.

The Equitable Total Chromatic Number of Some Join graphs

A proper total-coloring of graph G is said to be?equitable if the number of elements (vertices and edges) in any?two color classes differ by at most one, which the required?minimum number of colors is called the equitable total chromatic?number. In this paper, we prove some theorems on equitable?total coloring and derive the equitable total chromatic numbers?of Pm V?Sn, Pm V?Fn and Pm V Wn.

Vertex Distinguishing Equitable Total Chromatic Number of Join Graph

A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices＇ coloring sets are not identical and the difference of the elements colored by any two colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs Pn VPn, Cn VCn and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing equitable total are the same for join graphs Pn V Pn and Cn ∨ Cn.

A Class of Antimagic Join Graphs

A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2, ..., ｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G1 is an n-vertex graph with minimum degree at least r, and G2 is an m-vertex graph with maximum degree at most 2r - 1 （m ≥ n）, then G1 V G2 is antimagic.

Equitable Total Coloring of Some Join Graphs

The total chromatic number χt(G) of a graph G(V,E) is the minimum number of total independent partition sets of V E, satisfying that any two sets have no common element. If the difference of the numbers of any two total independent partition sets of V E is no more than one, then the minimum number of total independent partition sets of V E is called the equitable total chromatic number of G, denoted by χet(G). In this paper, we have obtained the equitable total chromatic number of Wm Kn, Fm Kn and Sm Kn whi...

Quantum search of many vertices on the joined complete graph

The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of many vertices on one low-connectivity graph,the joined complete graph.Our results reveal that,with the optimal jumping rate obtained from the theoretical method,we can find such target vertices at the time O(√N),where N is the number of total vertices.Therefore,the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.

一个调度Fork-Join任务图的最优算法(英文)

Fork-Join任务图是一种并行处理的基本结构.虽然许多算法在任务满足某些条件时能产生最优调度,但往往没有考虑节省处理器个数和减少任务集的总完成时间,从而降低算法的加速比和效率.因此,提出一种基于任务复制的平衡调度算法,其时间复杂度为O(vq+vlogv),v和q分别表示任务集中任务的个数和使用的处理器个数.通过分析已用处理器的负载和空闲时间段,把任务尽量分配到已用的处理器上以均衡负载,从而提高其利用率.实验结果表明,该算法的加速比和总体效率优于其他算法.因此,该算法对于高性能应用程序的调度是一个较好的选择.

调度Fork-Join任务图的贪心算法

任务调度算法的目标是把组成并行程序的一组任务分配到多个处理器以使得程序的完成时间最短,这是一个NP完全问题。虽然许多算法在任务满足某些条件时能产生最优调度,但大多都忽略了节省处理器个数和最小化程序总的完成时间等问题。Fork-Join结构是一种并行处理的基本结构。因此,专门针对Fork-Join任务图,提出了一个能产生最优调度的新的贪心调度算法,该算法具有高的加速比和总体效率,时间复杂度为2,其中,表示任务集中任务的个数。实验结果表明,相比其它算法,该算法具有较短的调度长度、较短的完成时间,使用的处理器数较少。

异构环境中Fork-Join任务图的调度算法

目前已有的Fork-Join任务图的调度算法大多假定处理机为同构的,而没有考虑实际应用中处理机的异构性以及节省处理机的问题,导致算法在具体应用中效率较低。因此,对Fork-Join任务图的调度问题进行研究,提出了一个基于异构环境的贪心调度算法,该算法具有高的加速比和总体效率,其时间复杂度为2,其中,表示任务集中任务的个数。实验结果表明,相比其它算法,该算法具有较短的调度长度、较短的完成时间,使用的处理机数较少,具有更强的实用性。

同构环境中Join任务图的一个调度算法

任务调度问题是一个NP完全问题。Join结构是一种并行处理的基本结构,虽然许多算法对Join任务图能产生最优调度,但大多都忽略了节省处理机个数和最小化程序总的完成时间等问题。因此,专门针对Join任务图,提出一个能产生最优调度的同构贪心调度算法,该算法具有高的加速比和总体效率,时间复杂度为O(v2),其中,v表示任务集中任务的个数。实验结果表明,相比其他算法,该算法具有较短的调度长度、较短的完成时间,使用的处理机数较少。

广义Fork-Join任务图的调度问题研究

Fork-Join结构是一种并行处理的基本结构。为处理传统方法难以解决的复杂和非线性问题,缩短整个程序的总完成时间,针对广义Fork-Join任务图提出了基于遗传算法的调度算法,该算法将遗传算法和任务复制相结合,有效地缩短了得到最优结果的时间。实验结果表明,与其他算法相比,该算法具有较短的调度长度。

基于通信竞争的Fork-Join任务图的调度算法

Fork-Join任务图是一种并行处理的基本结构,目前已有的Fork-Join任务图的调度算法大多没有考虑实际应用中通信链路的竞争及延迟以及节省处理机的问题,导致算法在具体应用中效率较低。因此,针对Fork-Join任务图,提出一个基于通信竞争的贪心调度算法,该算法具有高的加速比和总体效率,时间复杂度为O(vlogv),其中v表示任务集中任务的个数。实验结果表明,该算法相比其它算法具有较短的调度长度、较短的完成时间,使用的处理机数较少,具有更强的实用性。

通信竞争环境中Join任务图的一个调度算法

Join任务图是一种并行处理的基本结构。目前已有的Join任务图的调度算法大多忽略了通信链路的竞争、延迟以及节省处理机的问题,导致算法在实际应用中效率较低。针对这一问题,提出一个基于通信竞争的Join任务图的调度算法,该算法通过对各通信边的串行化而在任务调度中集成通信竞争,其时间复杂度为O(vlogv),其中v表示图中的任务数。实验结果表明,相比其他算法,该算法就调度长度、使用的处理机数、加速比和效率而言为优,具有更强的实用性。

Total Chromatic Number of the Join of K_(m,n) and C_n

The total chromatic number xT（G） of a graph G is the minimum number of colors needed to color the elements（vertices and edges） of G such that no adjacent or incident pair of elements receive the same color, G is called Type 1 if xT（G） =△（G）＋1. In this paper we prove that the join of a complete bipartite graph Km,n and a cycle Cn is of Type 1.

BMGSJoin:一种基于MapReduce的图相似度连接算法

图相似度连接在数据挖掘领域应用广泛,尤其是在数据预处理阶段,可用于数据清理、近复本检测等,其研究具有十分重要的意义.针对基于编辑距离约束的图相似度连接问题进行研究,返回两个图集合中所有编辑距离不超过给定阈值的图对.基于分布式编程框架MapReduce,设计采用"过滤-验证"框架的MGSJoin算法,利用基于路径的q-gram签名实现非解候选对的过滤,计数过滤.鉴于该算法键值对数量庞大的潜在问题,引入Bloom Filter技术对算法进行改进并设计BMGSJoin算法.实验结果表明,提出的两种图相似度连接算法能较大地改善现有算法的效率和可扩展性,并能较好地应对当前大数据挖掘分析的需求.

CCTD:一种通信限制下的Fork-Join任务调度算法

现代并行系统的复杂调度问题可以转化为Fork-join图的任务调度问题。然而在实际计算环境中,两个处理节点之间的通信大多以独占方式进行,现有的大多数任务调度算法往往忽略了对通信信道独占性的考虑。提出了一种带通信限制的Fork-join图调度算法CCTD。该算法引入了实际环境中的通信独占性限制,同时保证了Fork-join图的基于复制的优化调度,而且尽可能地减少了对处理器占用。实验结果表明,CCTD算法是一种适应性强的、高效的Fork-join图调度算法。

一个有效的Join任务图的调度算法

已有的Join任务图的调度算法大多不是基于通信竞争的环境而开发,且未考虑节省处理机的问题,使算法的应用效果不佳。因此,针对Join任务图,提出一个通信竞争环境的调度算法,该算法因串行通信边而改善其调度效率,时间复杂度为O(vlogv),其中,v为图中任务的个数。实验结果表明,与其他算法相比,该算法的调度长度较短且使用的处理机数较少,具有更高的加速比。

ON THE TOTAL COLORING OF GRAPH G ∨H

The total chromatic number XT(G) of graph G is the least number of colorsassigned to VE(G) such that no adjacent or incident elements receive the same color.Gived graphs G1,G2, the join of G1 and G2, denoted by G1∨G2, is a graph G, V(G) =V(GI)∪V(G2) and E(G) = E(G1)∪E(G2) ∪{uv | u∈(G1), v ∈ V(G2)}. In this paper, it's proved that if v(G) = v(H), both Gc and Hc contain perfect matching and one of the followings holds: (i)Δ(G) =Δ(H) and there exist edge e∈ E(G), e' E E(H)such that both G-e and H-e' are of Class l; (ii)Δ(G)<Δ(H) and there exixst an edge e ∈E(H) such that H-e is of Class 1, then, the total coloring conjecture is true for graph G ∨H.

On the First and Second Locating Zagreb Indices of Graphs

By the distance or degree of vertices of the molecular graph, we can define graph invariant called topological indices. Which are used in chemical graph to describe the structures and predicting some physicochemical properties of chemical compound? In this paper, by introducing two new topological indices under the name first and second Zagreb locating indices of a graph G, we establish the exact values of those indices for some standard families of graphs included the firefly graph.