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On the vulnerability of permutation graphs of complete and complete bipartite graphs
1991The integrity of a graph \(G\) is defined as \(\min\{| S|+m(G-S)\}\) taken over all subsets \(S\) of \(V(G)\), where \(m(G-S)\) is the order of the largest component of \(G-S\). The toughness of \(G\) is defined as \(\min\{| S|/w(G-S)\}\) taken over all disconnecting subsets \(S\) of \(G\), where \(w(G-S)\) is the number of components of \(G-S\).
Guichard, D. +2 more
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The genus of the complete multipartite graph and the complete multi-layered graph
ACS/IEEE International Conference on Computer Systems and Applications - AICCSA 2010, 2010The complete multipartite graph and the complete multi-layered graph are both generalizations of the complete bipartite graph. These two kinds of graphs have recursive structure and offer a very flexible choice of network size with respect to a fixed network order. This paper addresses the genus of the complete multipartite graph and the complete multi-
Saïd Bettayeb, Quan T. Nguyen
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Contractions to Complete Graphs
1988We survey some extremal problems concerning contraction to complete graphs, including two new theorems of the author. We also show an application to a conjecture of Las Vergnas and Meyniel.
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Edge disjoint graph spanners of complete graphs and complete digraphs
Proceedings of the Thirtieth Hawaii International Conference on System Sciences, 2002A spanning subgraph S=(V, E') of a connected simple graph (digraph)G=(V, E) is a f(x)-spanner if for any pair of nodes u and v, d/sub S/(u, v)/spl les/f(d/sub G/(u, v)) where d/sub G/ and d/sub S/ are the usual distance functions in graphs (digraphs) G and S, respectively. The delay of the f(x)-spanner is f(x)-x.
Christian Laforest +3 more
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Canadian Journal of Mathematics, 1967
In our paper “Magic graphs” (1) we showed that every complete graph Kn with n ⩾ 5 is “magic,” i.e., if the vertex set is indicated {vi} and if eij is the edge joining vi and vj, i ≠ j , then there exists a function α(eij) such that the set {α(eij)} consists of distinct positive rational integers and the vertex sums1have a constant value σ(α) for k = 1,
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In our paper “Magic graphs” (1) we showed that every complete graph Kn with n ⩾ 5 is “magic,” i.e., if the vertex set is indicated {vi} and if eij is the edge joining vi and vj, i ≠ j , then there exists a function α(eij) such that the set {α(eij)} consists of distinct positive rational integers and the vertex sums1have a constant value σ(α) for k = 1,
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THE TOTAL IRREGULARITY STRENGTH OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
Far East Journal of Mathematical Sciences (FJMS), 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tilukay, M. I. +3 more
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2011
Ranking of help functions with respect to their usefulness is in the main focus of this work. In this work a help function is regarded as useful to a student if the student has succeeded to solve a problem after using it. Methods from the theory of partial orderings are further applied facilitating an automated process of suggesting individualised ...
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Ranking of help functions with respect to their usefulness is in the main focus of this work. In this work a help function is regarded as useful to a student if the student has succeeded to solve a problem after using it. Methods from the theory of partial orderings are further applied facilitating an automated process of suggesting individualised ...
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Ars Comb., 1998
A packing in a graph is a set of pairwise edge-disjoint subgraphs of \(G\). The density of a packing is the ratio of the total number of edges in graphs of the packing and the number of edges of \(G\); its maximum is looked for. A complete graph \(K_n\) whose vertices are labelled by \(x_1,\ldots ,x_n\) is considered.
Lorenz Halbeisen, Norbert Hungerbühler
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A packing in a graph is a set of pairwise edge-disjoint subgraphs of \(G\). The density of a packing is the ratio of the total number of edges in graphs of the packing and the number of edges of \(G\); its maximum is looked for. A complete graph \(K_n\) whose vertices are labelled by \(x_1,\ldots ,x_n\) is considered.
Lorenz Halbeisen, Norbert Hungerbühler
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Decomposition of complete graphs into isomorphic complete bipartite graphs
2013Summary: A decomposition of a complete graph \(K\) into disjoint copies of a complete bipartite graph \(K_{s,t}\) is called a \(K_{s,t}\)-design of order \(n\). The existence problem of \(K_{s,t}\)-designs has been completely solved for the graphs \(K_{1,t}\) for \(k\geq 1\), \(K_{2^{a},2^{b}}\) for \(a,b\geq 1\), \(K_{2, 3}\) and \(K_{3, 3}\). In this
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Complete Graphs and Bipartite Graphs in a Random Graph
2021 5th International Conference on Vision, Image and Signal Processing (ICVISP), 2021Lijin Feng, Jackson Barr
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