Combinatorial labelings of graphs

Abstract

A (p, g)-graph G is said to be a permutation (combination) graph if G admits an assignment of distinct integers 1, 2, 3, ..., p to the vertices such that edge values obtained by the number of permutations (combinations) of larger vertex value taken smaller vertex value at a time are distinct. In this paper we obtain a necessary condition for combination graph and study structure of permutation and combination graphs which includes some open problems.