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Information Journal Paper

Title

Difference Labeling and Decomposition

Pages

  153-168

Abstract

 A difference labeling of a graph G is an injective function f: V (G) → N ∪ {0} together with the weight function f∗ on E(G) given by f∗(uv) = |f(u)-f(v)| for every edge uv in G. The collection of subgraphs induced by the edges of the same weight is a Decomposition of G and is called the common weight Decomposition of G induced by f. Let ϒf denote the collection of all the paths taken from each member of the common weight Decomposition induced by f. A difference labeling f of G is said to be a Graphoidal difference labeling if ϒf is an acyclic graphoidal Decomposition of G. This paper initiates a study on this concepts.

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