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2021
In this article, first we introduce six types of power graphs related to a graph (or directed graph), with the help of set theory.Then we show that these newly defined power graphs are pairwise distinct by a few examples. Finally, we discuss the relation between Eulerian being the base graph and these six power graph types.
Mokhtarian Dehkordi, Elham +3 more
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In this article, first we introduce six types of power graphs related to a graph (or directed graph), with the help of set theory.Then we show that these newly defined power graphs are pairwise distinct by a few examples. Finally, we discuss the relation between Eulerian being the base graph and these six power graph types.
Mokhtarian Dehkordi, Elham +3 more
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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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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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Graphs whose powers are chordal and graphs whose powers are interval graphs
Journal of Graph Theory, 1997The 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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Coloring Powers of Planar Graphs
SIAM Journal on Discrete Mathematics, 2003Summary: 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.
Agnarsson, Geir +1 more
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On the Power of Graph Searching for Cocomparability Graphs
SIAM Journal on Discrete Mathematics, 2016Summary: 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
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Induced Matching Extendable Graph Powers
Graphs and Combinatorics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Coloring Powers of Chordal Graphs
SIAM Journal on Discrete Mathematics, 2004Summary: We prove that the \(k\)th 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 \(k\)th power of \(G\).
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Linear Algebra and its Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ma, Xiaobin, Geng, Xianya
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ma, Xiaobin, Geng, Xianya
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Applying Power Graph Analysis to Weighted Graphs
2012We expanded Power Graph Analysis for use with weighted graphs, applying the technique to document categorisation with promising results. With the additional weight information we were able to create more accurate representations of the underlying data while maintaining a high level of edge reduction and improving visualisation of the graph.
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