Displaying similar documents to “The Dynamics of the Forest Graph Operator”

On the tree graph of a connected graph

Ana Paulina Figueroa, Eduardo Rivera-Campo (2008)

Discussiones Mathematicae Graph Theory

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Let G be a graph and C be a set of cycles of G. The tree graph of G defined by C, is the graph T(G,C) that has one vertex for each spanning tree of G, in which two trees T and T' are adjacent if their symmetric difference consists of two edges and the unique cycle contained in T ∪ T' is an element of C. We give a necessary and sufficient condition for this graph to be connected for the case where every edge of G belongs to at most two cycles in C.

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. ...