The Inertia Indexes of One Special Kind of Tricyclic Graphs - Applied Mathematics

AM > Vol.10 No.1, January 2019

The Inertia Indexes of One Special Kind of Tricyclic Graphs ()

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DOI: 10.4236/am.2019.101002 893 Downloads 1,615 Views

Author(s)

Haicheng Ma^*, Chengling Xie

Affiliation(s)

Department of Mathematics, Qinghai University for Nationalities Xining, Qinghai, China.

ABSTRACT

Let G be a graph and A=(a_ij)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.

KEYWORDS

Tricyclic Graphs, Positive Inertia Index, Negative Inertia Index, Nullity

Share and Cite:

Ma, H. and Xie, C. (2019) The Inertia Indexes of One Special Kind of Tricyclic Graphs. Applied Mathematics, 10, 11-18. doi: 10.4236/am.2019.101002.

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