Some New Combination Graphs

Abstract

A graph $G=(V,E)$ with $p$ vertices and $q$ edges is said to be combination graph, if there exists an injection $f:V(G)\rightarrow{}\{1,2,\ldots,p\}$ such that the induced edge function $g_{f}:E(G)\rightarrow \mathbb{N}$ defined by $g_{f}(uv)=\frac{(f(u))!}{| f(u)-f(v)|! (f(v))!} ( f(u)>f(v))$, for every $uv$ $ \in $ $E(G)$ is injective. In this paper we prove that some cycle and wheel related graphs obtained with the use of graph operations are combination graph.