2013/06/29 by Guihai Yu, Xiao‐Dong Zhang, Yu, Guihai +4 · 3 citations
Chemistry · Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #math.CO #msc:05C50
paper · pdf · doi:10.48550/arxiv.1307.0059
23 pages, 8figures
arxiv created 2013/06/29 · openalex publication_date 2013/06/29 · arxiv updated 2013/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Gw be a weighted graph. The inertia of Gw is the triple In(Gw)=(i+(Gw),i-(Gw), i0(Gw)), where i+(Gw),i-(Gw),i0(Gw) are the number of the positive, negative and zero eigenvalues of the adjacency matrix A(Gw) of Gw including their multiplicities, respectively. i+(Gw), i-(Gw) is called the positive, negative index of inertia of Gw, respectively. In this paper we present a lower bound for the positive, negative index of weighted unicyclic graphs of order n with fixed girth and characterize all weighted unicyclic graphs attaining this lower bound. Moreover, we characterize the weighted unicyclic graphs of order n with two positive, two negative and at least n-6 zero eigenvalues, respectively.