Bipartite graphs with at most six non-zero eigenvalues
نویسندگان
چکیده
منابع مشابه
COSPECTRALITY MEASURES OF GRAPHS WITH AT MOST SIX VERTICES
Cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. Actually, the origin of this concept came back to Richard Brualdi's problems that are proposed in cite{braldi}: Let $G_n$ and $G'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2...
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cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. actually,the origin of this concept came back to richard brualdi's problems that are proposed in cite{braldi}:let $g_n$ and $g'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2 g...
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For a graph G of order n and with eigenvalues λ1 > · · · > λn, the HL-index R(G) is defined as R(G) = max { |λb(n+1)/2c|, |λd(n+1)/2e| } . We show that for every connected bipartite graph G with maximum degree ∆ > 3, R(G) 6 √ ∆− 2 unless G is the the incidence graph of a projective plane of order ∆− 1. We also present an approach through graph covering to construct infinite families of bipartit...
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The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
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Let $G$ be a graph with eigenvalues $lambda_1(G)geqcdotsgeqlambda_n(G)$. In this paper we find all simple graphs $G$ such that $G$ has at most twelve vertices and $G$ has exactly two non-negative eigenvalues. In other words we find all graphs $G$ on $n$ vertices such that $nleq12$ and $lambda_1(G)geq0$, $lambda_2(G)geq0$ and $lambda_3(G)0$, $lambda_2(G)>0$ and $lambda_3(G)
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2016
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.749.264