United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SOME RELATIONS BETWEEN RANK, CHROMATIC NUMBER AND ENERGY OF GRAPHS
United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SOME RELATIONS BETWEEN RANK, CHROMATIC NUMBER AND ENERGY OF GRAPHS
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发表时间：
2006
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通讯作者：
S. Akbari;Abdus Salam;E. Ghorbani
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作者：
S. Akbari;Abdus Salam;E. Ghorbani
图G的能量定义为G的所有特征值的绝对值之和，用E(G)表示。设G是一个图，rank(G)是G的邻接矩阵的秩。本文刻画了所有E(G) = rank(G)的图。在其他结果中，我们表明除了少数图族外，E(G)≥2 max(χ(G), n - χ(G))，其中G和χ(G)分别是G的补数和色数。并且给出了E(G)在秩(G)上的一些新的下界。
The energy of a graph G is defined as the sum of the absolute values of all eigenvalues of G and denoted by E(G). Let G be a graph and rank(G) be the rank of the adjacency matrix of G. In this paper we characterize all the graphs with E(G) = rank(G). Among other results we show that apart from a few families of graphs, E(G) ≥ 2 max(χ(G), n − χ(G)), where G and χ(G) are the complement and the chromatic number of G, respectively. Moreover some new lower bounds for E(G) in terms of rank(G) are given.