Small graphs with exactly two non-negative eigenvalues
نویسندگان
چکیده
منابع مشابه
Unicyclic graphs with exactly two main eigenvalues
An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero, and it is well known that a graph has exactly one main eigenvalue if and only if it is regular. In this work, all connected unicyclic graphs with exactly two main eigenvalues are determined. c © 2006 Elsevier Ltd. All rights reserved.
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In this note, we consider connected graphs with exactly two main eigenvalues. We will give several constructions for them, and as a consequence we show a family of those graphs with an unbounded number of distinct valencies.
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where ni = nβ 2 i (i = 1, 2); β1 and β2 denote the main angles of μ1 and μ2, respectively. Further, let G be any connected or disconnected graph (not necessarily with two main eigenvalues). Let S be any subset of the vertex set V (G) and let GS be the graph obtained from the graph G by adding a new vertex x which is adjacent exactly to the vertices from S. If σ(GS1) = σ(GS2) then we prove that ...
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The non-commuting graph $Gamma(G)$ of a non-abelian group $G$ with the center $Z(G)$ is a graph with thevertex set $V(Gamma(G))=Gsetminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent in $Gamma(G)$if and only if $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.
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ژورنال
عنوان ژورنال: Algebraic structures and their applications
سال: 2017
ISSN: 2382-9761,2423-3447
DOI: 10.29252/asta.4.1.1