Displaying similar documents to “On the Graph for which there is a Tree as the Inverse Interchange Graph of a Local Graph.”

The Dynamics of the Forest Graph Operator

Suresh Dara, S.M. Hegde, Venkateshwarlu Deva, S.B. Rao, Thomas Zaslavsky (2016)

Discussiones Mathematicae Graph Theory

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In 1966, Cummins introduced the “tree graph”: the tree graph T(G) of a graph G (possibly infinite) has all its spanning trees as vertices, and distinct such trees correspond to adjacent vertices if they differ in just one edge, i.e., two spanning trees T1 and T2 are adjacent if T2 = T1 − e + f for some edges e ∈ T1 and f ∉ T1. The tree graph of a connected graph need not be connected. To obviate this difficulty we define the “forest graph”: let G be a labeled graph of order α, finite...

Clique graph representations of ptolemaic graphs

Terry A. Mckee (2010)

Discussiones Mathematicae Graph Theory

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A graph is ptolemaic if and only if it is both chordal and distance-hereditary. Thus, a ptolemaic graph G has two kinds of intersection graph representations: one from being chordal, and the other from being distance-hereditary. The first of these, called a clique tree representation, is easily generated from the clique graph of G (the intersection graph of the maximal complete subgraphs of G). The second intersection graph representation can also be generated from the clique graph,...