Positive and negative inertia indexes and nullity of two kinds of tricyclic graphs
MENG Xia-fei, MA Hai-cheng, LI Sheng-gang*
(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)
Abstract:
The problem how to calculate the positive and negative inertia indexes and nullity of one-type and two-type tricyclic graphs are studied. By means of deleting pendant trees and compressing internal paths, a method of calculating the positive and negative inertia indexes and nullity of the two special kinds of tricyclic graphs are given.It is proved that the positive and negative inertia indexes and nullity of one-type tricyclic graphs equal to the sum of those of some trees and bicyclic graphs, respectively; the positive and negative inertia indexes and nullity of two-type tricyclic graphs equal to the sum of those of some trees and simple tricyclic graphs respectively; the positive and negative inertia indexes and nullity of these simple tricyclic graphs can be calculated by Matlab.For one-type and two-type tricyclic graphs,a conjecture about difference of the positive and negative inertia index of a graph is verified.
KeyWords:
tricyclic graph; positive inertia index; negative inertia index; nullity
