Results 221 to 230 of about 5,865,138 (250)

Graphs whose powers are chordal and graphs whose powers are interval graphs

Journal of Graph Theory, 1997
The main theorem of this paper gives a forbidden induced subgraph condition on \(G\) that is sufficient for chordality of \(G^m\). This theorem is a generalization of a theorem of Balakrishnan and Paulraja who had provided this only for \(m=2\).
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Power graphs

J. Inf. Process. Cybern., 1994
Summary: Graphs with vertex set \(V\) can be ``lifted'' to the power set \(V^\#= {\mathcal P}(V)\backslash \{\varnothing\}\). In this paper graphs and their properties, in particular automorphisms and isomorphisms, are studied with respect to this power construction.
Ulrike Baumann, Reinhard Pöschel, Irmgard Schmeichel   +2 more
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On the Power Graph and the Reduced Power Graph of a Finite Group

Communications in Algebra, 2019
In this paper, for a finite group, we investigate to what extent its directed (resp. undirected) reduced power graph determines its directed power graph (resp. reduced power graph).
Rajendran Rajkumar, Anitha Thangamani
exaly   +2 more sources

Power Domination in Product Graphs

SIAM Journal on Discrete Mathematics, 2008
The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number $\gamma_P(G)$ of G is the minimum cardinality of a power dominating set. Dorfling and Henning [Discrete Appl.
Dorbec, Paul, Klavzar, Sandi, Mollard, Michel, Spacapan, Simon   +3 more
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The Chromatic Number of Graph Powers

Combinatorics, Probability and Computing, 2002
It is shown that the maximum possible chromatic number of the square of a graph with maximum degree d and girth g is (1 + o (1)) d 2 if
Noga Alon, Bojan Mohar
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Unleashing the Power of Information Graphs

ACM SIGMOD Record, 2015
Information graphs are generic graphs that model different types of information through nodes and edges. Knowledge graphs are the most common type of information graphs in which nodes represent entities and edges represent relationships among them.
Matteo Lissandrini, Davide Mottin, Themis Palpanas, Dimitra Papadimitriou, Yannis Velegrakis   +4 more
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Powers of graphs

Proceedings of the sixteenth annual ACM symposium on Theory of computing - STOC '84, 1984
In this paper we investigate a powerful, and yet simple, technique for devising approximation algorithms for a wide variety of NP-complete problems in routing, location, and communication network design. Each of the algorithms presented here delivers an approximate solution guaranteed to be within a constant factor of the optimal solution. In addition,
Dorit S. Hochbaum, David B. Shmoys
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Coloring Powers of Chordal Graphs

SIAM Journal on Discrete Mathematics, 2004
We prove that the kth power G k of a chordal graph G with maximum degree $\Delta$ is $O(\sqrt{k}\Delta^{(k+1)/2})$-degenerate for even values of k and $O(\Delta^{(k+1)/2})$-degenerate for odd values. In particular, this bounds the chromatic number $\chi(G^k)$ of the kth power of G.
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Comparing the Power of Games on Graphs

Mathematical Logic Quarterly, 1997
AbstractThe descriptive complexity of a problem is the complexity of describing the problem in some logical formalism. One of the few techniques for proving separation results in descriptive complexity is to make use of games on graphs played between two players, called the spoiler and the duplicator. There are two types of these games, which differ in
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A Review of Graph Neural Networks and Their Applications in Power Systems

Journal of Modern Power Systems and Clean Energy, 2022
Birgitte Bak-Jensen, Jayakrishnan Radhakrishna Pillai, Wenlong Liao   +2 more
exaly