Displaying similar documents to “Effect of edge-subdivision on vertex-domination in a graph”

The edge C₄ graph of some graph classes

Manju K. Menon, A. Vijayakumar (2010)

Discussiones Mathematicae Graph Theory

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The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices,...

Recognizing Chordal Graphs: Lex BFS and MCS 1

Broderick Arneson, Piotr Rudnicki (2006)

Formalized Mathematics

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We are formalizing the algorithm for recognizing chordal graphs by lexicographic breadth-first search as presented in [13, Section 3 of Chapter 4, pp. 81-84]. Then we follow with a formalization of another algorithm serving the same end but based on maximum cardinality search as presented by Tarjan and Yannakakis [25].This work is a part of the MSc work of the first author under supervision of the second author. We would like to thank one of the anonymous reviewers for very useful suggestions. ...

On transitive orientations of G-ê

Michael Andresen (2009)

Discussiones Mathematicae Graph Theory

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A comparability graph is a graph whose edges can be oriented transitively. Given a comparability graph G = (V,E) and an arbitrary edge ê∈ E we explore the question whether the graph G-ê, obtained by removing the undirected edge ê, is a comparability graph as well. We define a new substructure of implication classes and present a complete mathematical characterization of all those edges.