TITLE:
The Inertia Indexes of One Special Kind of Tricyclic Graphs
AUTHORS:
Haicheng Ma, Chengling Xie
KEYWORDS:
Tricyclic Graphs, Positive Inertia Index, Negative Inertia Index, Nullity
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.1,
January
29,
2019
ABSTRACT: Let G be a graph and A=(aij)n×n be the adjacency matrix of G, the eigenvalues of A are said to be the eigenvalues of the graph G, and to form the spectrum of
this graph. The numbers of positive, negative and zero eigenvalues in the spectrum of the graph G are called positive and negative inertia indexes and nullity of the graph G, are denoted by p(G), n(G), η(G), respectively, and are collectively called inertia indexes of the graph G. The inertia indexes have many important applications in chemistry and mathematics. The purpose of the research of this paper is to calculate the inertia indexes of one special kind of tricyclic graphs. A new calculation method of the inertia indexes of this tricyclic graphs with large vertices is given, and the inertia indexes of this tricyclic graphs with fewer
vertices can be calculated by Matlab.