Maximum nullity of outerplanar graphs and the path cover number

J.H. Sinkovic

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)

Abstract

Let G=(V,E) be a graph with V={1,2,…,n}. Define S(G) as the set of all n×n real-valued symmetric matrices A=[aij] with aij¿0,i¿j if and only if ijeE. By M(G) we denote the largest possible nullity of any matrix AeS(G). The path cover number of a graph G, denoted P(G), is the minimum number of vertex disjoint paths occurring as induced subgraphs of G which cover all the vertices of G. There has been some success with relating the path cover number of a graph to its maximum nullity. Johnson and Duarte [5], have shown that for a tree T,M(T)=P(T). Barioli et al. [2], show that for a unicyclic graph G,M(G)=P(G) or M(G)=P(G)-1. Notice that both families of graphs are outerplanar. We show that for any outerplanar graph G,M(G) =P(G). Further we show that for any partial 2-path G,M(G)=P(G).
Original languageEnglish
Pages (from-to)2052-2060
JournalLinear Algebra and Its Applications
Volume432
Issue number8
DOIs
Publication statusPublished - 2010

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