Results 191 to 200 of about 1,046 (212)
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Total colorings of circulant graphs
Discrete Mathematics, Algorithms and Applications, 2020The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text]
J. Geetha 0001 +2 more
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A SURVEY ON UNDIRECTED CIRCULANT GRAPHS
Discrete Mathematics, Algorithms and Applications, 2012Circulant 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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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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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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On the Partition Dimension of Circulant Graphs
The Computer Journal, 2016For 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 +3 more
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Reliability analysis of circulant graphs
Networks, 1998Summary: 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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The Kirchhoff Indices for Circulant Graphs
Siberian Mathematical JournalzbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. D. Mednykh, I. A. Mednykh
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Self-complementary circulant graphs
Ars Comb., 1999Summary: 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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On the Ádám Conjecture on Circulant Graphs
1998In 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 +2 more
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Kernel in Oriented Circulant Graphs
2009A 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 +3 more
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