Results 141 to 150 of about 590,064 (163)

Line graphs and circulants

Ars Comb., 2012
Summary: The line graph of \(G\), denoted \(L(G)\), is the graph with vertex set \(E(G)\), where vertices \(x\) and \(y\) are adjacent in \(L(G)\) iff edges \(x\) and \(y\) share a common vertex in \(G\). In this paper we determine all graphs \(G\) for which \(L(G)\) is a circulant graph.
Jason I. Brown, Richard Hoshino
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A SURVEY ON UNDIRECTED CIRCULANT GRAPHS

Discrete Mathematics, Algorithms and Applications, 2012
Circulant graphs have been extensively investigated over the past 30 years because of their broad application to different fields of theory and practice. Two known surveys on circulant networks including a survey on undirected circulants have been published: by Bermond et al. [Distributed loop computer networks: A survey, J.
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On the Partition Dimension of Circulant Graphs

The Computer Journal, 2016
For a vertex v of a connected graph G ( V , E ) and a subset S of V , the distance between v and S is defined by d ( v , S )=min{ d ( v , x ):x∈ S }. For an ordered k .-partition Π={ S 1 , S 2 ,…, S k } of V , the representation of v with respect to Π is the k -vector r ( v ∣Π)=( d ( v , S 1 ), d ( v , S 2 ),…, d ( v , S k )).
Cyriac Grigorious, Sudeep Stephen, Bharati Rajan, Mirka Miller   +3 more
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Reliability analysis of circulant graphs

Networks, 1998
Summary: The circulant graphs are of particular interest as models of communication networks. In this work, we present new reliability analysis results for circulants based on the concept of restricted edge connectivity, which generalizes the super-\(\lambda\) property of a graph. We evaluate the restricted edge connectivity \(\lambda'\) and the number
Qiaoliang Li, Qiao Li
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Pancyclicity of recursive circulant graphs

Information Processing Letters, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Toru Araki, Yukio Shibata
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On the Ádám Conjecture on Circulant Graphs

1998
In this paper we study isomorphism between circulant graphs. Such graphs have a vast number of applications to telecommunication network, VLSI design and distributed computation [4,13,15,17]. By suitably choosing the length of the chord between two nodes of the network, one can achieve the appropriate property: e.g., low diameter, high connectivity, or
Bernard Mans, Francesco Pappalardi, Igor E. Shparlinski   +2 more
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The Kirchhoff Indices for Circulant Graphs

Siberian Mathematical Journal
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. D. Mednykh, I. A. Mednykh
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Pancyclicity of connected circulant graphs

Journal of Graph Theory, 1996
The following results are shown for connected circulant graphs \(G\): (1) If \(G\) has at least two jumps, then every edge of \(G\) lies in a cycle of each even length \(i, i\geq 4\). (2) If the smallest cycle of \(G\) is a triangle, then \(G\) is pancyclic. To show these results, cycles of the specified lengths are all explicitly given.
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Kernel in Oriented Circulant Graphs

2009
A kernel in a directed graph D(V,E) is a set S of vertices of D such that no two vertices in S are adjacent and for every vertex u in $V\smallsetminus S$ there is a vertex v in S , such that (u,v) is an arc of D. The problem of existence of a kernel is NP-complete for a general digraph.
Paul D. Manuel, Indra Rajasingh, Bharati Rajan, Joice Punitha   +3 more
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Self-complementary circulant graphs

Ars Comb., 1999
Summary: There exists a self-complementary circulant graph with \(n\) vertices if and only if every prime \(p\) in the prime factorization of \(n\) satisfies \(p \equiv 1\) (mod 4).
Brian Alspach, Joy Morris, V. Vilfred
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