The Cayley Sum Graph of Ideals of a Lattice

Let L be a lattice, I(L) be the set of ideals of L and S be a subset of I(L). In this paper,we introduce an undirected Cayley graph of L, denoted by L;S with elements of I(L) as thevertex set and for two distinct vertices I and J, I is adjacent to J if and only if there is an element k of S such that I_K = J or J _K = I. We study some basic properties of the graph L;S such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of L;S.

Keywords:

Lattice , Cayley graph , Ring graph , Outerplanar graph