The extremal problems on the inertia of weighted bicyclic graphs

2013/11/13 by Shibing Deng, Shuchao Li, Deng, Shibing +3
Mathematics · #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C50 #msc:15A18

paper · pdf · doi:10.48550/arxiv.1311.3049

12 pages, 5 figures, 2 tables. arXiv admin note: text overlap with arXiv:1307.0059 by other authors

arxiv created 2013/11/13 · arxiv updated 2013/11/14

Abstract

Let G_w be a weighted graph. The number of the positive, negative and zero eigenvalues in the spectrum of G_w are called positive inertia index, negative inertia index and nullity of G_w, and denoted by i₊(G_w), i_-(G_w), i₀(G_w), respectively. In this paper, sharp lower bound on the positive (resp. negative) inertia index of weighted bicyclic graphs of order n with pendant vertices is obtained. Moreover, all the weighted bicyclic graphs of order n with at most two positive, two negative and at least n-4 zero eigenvalues are identified, respectively.

Citations

• The inertia of weighted unicyclic graphs

Related

• On the positive and negative inertia of weighted graphs
• The inertia of weighted unicyclic graphs
• The relationship between the negative inertia index of graph G and its girth g and diameter d
• On graphs with exactly two positive eigenvalues
• Connected signed graphs with given inertia indices and given girth