Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773286 | Linear Algebra and its Applications | 2017 | 13 Pages |
Abstract
Let G be a graph and let A(G) be adjacency matrix of G. The positive inertia index (respectively, the negative inertia index) of G, denoted by p(G) (respectively, n(G)), is defined to be the number of positive eigenvalues (respectively, negative eigenvalues) of A(G). In this paper, we present the bounds for p(G) and n(G) as follows:m(G)âc(G)â¤p(G)â¤m(G)+c(G),m(G)âc(G)â¤n(G)â¤m(G)+c(G), where m(G) and c(G) are respectively the matching number and the cyclomatic number of G. Furthermore, we characterize the graphs which attain the upper bounds and the lower bounds respectively.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yi-Zheng Fan, Long Wang,