Minimum number of distinct eigenvalues of graphs
نویسندگان
چکیده
منابع مشابه
Ela Minimum Number of Distinct Eigenvalues of Graphs∗
The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to deduce further properties of q(G). It is shown that there is a great number of graphs G for which q(G) = 2. For some families of graphs, such as the join of a graph with itself,...
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For a given graph G and an associated class of real symmetric matrices whose offdiagonal entries are governed by the adjacencies in G, the collection of all possible spectra for such matrices is considered. Building on the pioneering work of Colin de Verdière in connection with the Strong Arnold Property, two extensions are devised that target a better understanding of all possible spectra and ...
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In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
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The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...
متن کاملThe minimum number of distinct eigenvalues among the symmetric matrices with a given graph
A classic result is that the number of distinct eigenvalues of a graph of diameter d is at least d+1. More generally, let G be a graph with n vertices, and let S(G) denote the set of all symmetric n by n matrices, A = [aij ], with the property that for off-diagonal entries, aij is nonzero if and only if G has an edge from i to j. The traditional proof of the classic result extends to A ∈ S(G). ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2013
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1679