Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415967 | Linear Algebra and its Applications | 2016 | 15 Pages |
Abstract
Let G be a simple graph with vertex set V(G) and edge set E(G). The signature s(G) of G is the difference between the number of positive eigenvalues and the number of negative eigenvalues of the adjacency matrix A(G). In [20], it was proved that âc1(G)â¤s(G)â¤c1(G), where c1(G) denotes the number of odd cycles in G. A problem arises naturally: What graphs have signature attaining the upper bound c1(G) (resp., the lower bound âc1(G))? In this paper, we focus our attention on this problem, characterizing graphs G whose signature equals c1(G) (resp., âc1(G)).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xiaobin Ma, Dein Wong, Fenglei Tian,