Results 231 to 240 of about 254,638 (264)

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).
R Rajkumar, T Anitha
exaly   +2 more sources

On the Power of Graph Searching for Cocomparability Graphs

SIAM Journal on Discrete Mathematics, 2016
Summary: In this paper we study how graph searching on a cocomparability graph \(G\) can be used to produce cocomp orderings (i.e., orderings that are linear extensions of some transitive orientation of \(\overline{G}\)) that yield simple algorithms for various intractable problems in general.
Corneil, Derek G.   +3 more
openaire   +2 more sources

Coloring Powers of Planar Graphs

SIAM Journal on Discrete Mathematics, 2003
Summary: We give nontrivial bounds for the inductiveness or degeneracy of power graphs \(G^{k}\) of a planar graph \(G\). This implies bounds for the chromatic number as well, since the inductiveness naturally relates to a greedy algorithm for vertex-coloring the given graph.
Geir Agnarsson, Magnús M. Halldórsson
openaire   +4 more sources

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 \(m=2\).
openaire   +2 more sources

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   +2 more
openaire   +1 more source

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))d2 if g = 3, 4, 5 or 6, and is Θ(d2 / log d) if g [ges ] 7. Extensions to higher powers are considered as well.
Noga Alon, Bojan Mohar
openaire   +2 more sources

Home - About - Disclaimer - Privacy