Results 11 to 20 of about 3,489,698 (302)
Discrete Mathematics, 1998 Let \(G\) be a simple graph. The clique graph \(K(G)\) is the intersection graph of the maximal cliques of \(G\). A vertex in \(G\) is universal if it is adjacent to all other vertices in \(G\). The \(n\)th iterated clique graph of \(G\) is defined by \(K^{(n)}= K(K^{n-1} (G))\) and \(G\) is \(n\)-convergent if \(K^n (G)\) is isomorphic to the one ...
Cláudio Leonardo Lucchesi +2 more
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k-L(2, 1)-labelling for planar graphs is NP-complete for k>=4 [PDF]
, 2009 A mapping from the vertex set of a graph G=(V,E) into an interval of integers {0,...,k} is an L(2,1)-labelling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common ...
Havet, F, Eggemann, N, Noble, S D
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Treewidth of the Line Graph of a Complete Graph [PDF]
Journal of Graph Theory, 2014 Abstract In recent articles by Grohe and Marx, the treewidth of the line graph of a complete graph is a critical example—in a certain sense, every graph with large treewidth “contains” .
Daniel J. Harvey, David R. Wood
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Ultrametrics and Complete Multipartite Graphs
Theory and Applications of Graphs, 2022 Let \((X, d)\) be a semimetric space and let \(G\) be a graph. We say that \(G\) is the diametrical graph of \((X, d)\) if \(X\) is the vertex set of \(G\) and the adjacency of vertices \(x\) and \(y\) is equivalent to the equality \(\diam X = d(x, y)\).
Viktoriia Viktorivna Bilet +2 more
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Computational graph completion
Research in the Mathematical Sciences, 2022 34 pages.
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Hamilton Cycles in Bidirected Complete Graphs [PDF]
, 2022 Zaslavsky observed that the topics of directed cycles in directed graphs and alternating cycles in edge 2-colored graphs have a common generalization in the study of coherent cycles in bidirected graphs. There are classical theorems by Camion, Harary and
Busch, Arthur +2 more
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On the ranks of configurations on the complete graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We consider the parameter rank introduced for graph configurations by M. Baker and S. Norine. We focus on complete graphs and obtain an efficient algorithm to determine the rank for these graphs.
Robert Cori, Yvan Le Borgne
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Monochromatic triangles in three-coloured graphs [PDF]
, 2013 In 1959, Goodman [9] determined the minimum number of monochromatic triangles in a complete graph whose edge set is 2-coloured. Goodman (1985) [10] also raised the question of proving analogous results for complete graphs whose edge sets are coloured ...
Král', D. +16 more
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Seidel Integral Complete Split Graphs [PDF]
Mathematics Interdisciplinary Research, 2019 In the paper we consider a generalized join operation, that is, the H-join on graphs where H is an arbitrary graph. In terms of Seidel matrix of graphs we determine the Seidel spectrum of the graphs obtained by this operation on regular graphs.
Pavel Hic +2 more
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Constructions of new integral graph families
Electronic Journal of Graph Theory and Applications, 2021 We construct new families of integral graphs by considering complete products, unions and point identifications of complete graphs and complete bipartite graphs.
Thomas Gardemann, Katja Mönius
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