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.
Highlights
Throughout the paper, graphs are simple, without loops and multiple edges
( ) 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 purpose of the research of this paper is to calculate the inertia indexes of one special kind of tricyclic graphs
Summary
In [3]-[19], the inertia indexes is researched as several kinds of graphs such as trees, unicyclic graphs, bicyclic graphs and tricyclic graphs. The inertia indexes of a special kinds of tricyclic graphs different from literatures [20] [21] are studied, and a new calculation method is given by deleting pendant trees and compressing internal paths and Matlab software. Let G be a connected graph of order n, the graphs respectively with size n −1 , n, n +1 and n + 2 are called the tree, the unicycle graph, the bicycle graph and tricyclic graph. For a given tricycle graph G ∈ γ , the only induced subgraph ζ-graphs is called the kernel of graph G, as χ (G)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
