Integral circulant graphs of prime power order with maximal energy
J.W. Sander,Torsten Sander +1 more
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In this article, the maximal energy of integral circulant graphs of prime power order ps and varying divisor sets was analyzed and the main result was that this maximal energy approximately lies between s(p-1)ps-1 and twice this value.About:
This article is published in Linear Algebra and its Applications.The article was published on 2011-12-15 and is currently open access. It has received 18 citations till now. The article focuses on the topics: Maximal independent set & Divisor.read more
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Eigenvalues of Cayley graphs
Xiaogang Liu,Sanming Zhou +1 more
TL;DR: A survey of the known results on eigenvalues of Cayley graphs and their applications can be found in this article, together with related results on Cayley digraphs and generalizations of the Cayley graph.
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Spectral Properties of Unitary Cayley Graphs of Finite Commutative Rings
Xiaogang Liu,Sanming Zhou +1 more
TL;DR: The necessary and sufficient conditions for a regular Cayley graph to be Ramanujan were given in this article, and the spectral moments of the line graph of the graph were derived.
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The energy of random graphs
Wenxue Du,Xueliang Li,Yiyang Li +2 more
TL;DR: In this paper, an exact estimate of the energy of random bipartite graphs G n (p) was established, by using the Wigner semicircle law for any probability p. But only a few graphs attain the equalities in these bounds.
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The maximal energy of classes of integral circulant graphs
J.W. Sander,Torsten Sander +1 more
TL;DR: The energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Z"n and edge set {{a,b}:a,[email protected]?Z"n,gcd(a-b,n)@?D}.
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Quadratic unitary Cayley graphs of finite commutative rings
TL;DR: In this paper, the spectral properties of a family of Cayley graphs on finite commutative rings were studied, and the spectral moments of these graphs were determined under the condition that |R i | / | M i | ≡ 1 ( mod 4 ) for 1 ≤ i ≤ s.
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Journal ArticleDOI
The energy of a graph
TL;DR: In this article, it was shown that for any positive integer n⩾3, there exist two equienergetic graphs of order 4n that are not cospectral.
Book
Handbook of convex geometry
Peter M. Gruber,Jörg M. Wills +1 more
TL;DR: This handbook should be useful for mathematicians working in other areas, as well as for econometrists, computer scientists, crystallographers, physicists and engineers who are looking for geometric tools for their own work.
Journal ArticleDOI
The energy of graphs and matrices
TL;DR: In this article, the concept of graph energy was introduced by Gutman and Koolen and Moulton, and it was shown that Wigner's semicircle law implies that E(G ) = ( 4 3 π + o ( 1 ) ) n 3 / 2 for almost all graphs G.
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Maximal Energy Graphs
Jack H. Koolen,Vincent Moulton +1 more
TL;DR: It is shown that if G is a graph on n vertices, then E(G)@?n21+n must hold, and an infinite family of graphs for which this bound is sharp is given.