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Strongly multiplicative graphs

L.W. Beineke;  S.M. Hegde — 2001

Discussiones Mathematicae Graph Theory

A graph with p vertices is said to be strongly multiplicative if its vertices can be labelled 1,2,...,p so that the values on the edges, obtained as the product of the labels of their end vertices, are all distinct. In this paper, we study structural properties of strongly multiplicative graphs. We show that all graphs in some classes, including all trees, are strongly multiplicative, and consider the question of the maximum number of edges in a strongly multiplicative graph of a given order.

The Dynamics of the Forest Graph Operator

Suresh Dara;  S.M. Hegde;  Venkateshwarlu Deva;  S.B. Rao;  Thomas Zaslavsky — 2016

Discussiones Mathematicae Graph Theory

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 or infinite,...

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