Monophonic Wirelength in Graph Embedding

Abstract

In this paper we consider the monophonic embedding ofcirculant networks into cycles and we produce an algorithmto get the monophonic wirelength of the same.Further wend that the monophonic wirelength of some family of cir-In this paper, we define the monophonic embedding of graph G into another graph H and this paper presents a monophonic algorithm to find the monophonic wirelength of circulant networks G[n, ±S], where S ⊆ {1,2,3,…,n/2} into the family of Cycle Cn, n≥ 4. The mono-phonic embedding of a graph G into a graph H is an embedding denoted by fmis a bijective map from the vertex set of G into the vertex set of H and fm is a one-one mapping from the edge set (x, y) of G into Pm(H) where Pm(H) is the set of monophonic paths between fm(x) and fm(y) for every fm(x), fm(y) ∈ H. The monophonic wirelength of fm of G into H is the sum of distances of monophonic paths between two vertices fm(x) and fm(y) in H such that (x, y) ∈ E(G). In addition, the eccentricity, radius and diameter of an embedding of G into H are defined. The average wirelength of an embedding is defined and the bounds of average wirelength of some embeddings have been found.