Hamming Index for Several Graph Classes Produced by an Side-Node Incidence Matrix

Abstract

For example G(V,E) becomes graph on p nodes and q sides and B’(G) called being side-node incidence matrix from G. Every side e of G can be labeled using a binary digit string of length n from the row of B’(G) which corresponds to the side e, denoted by s(e). The Hamming distance between the strings s(e) and s(f) of length n is defined to be the number of positions of s(e) and s(f) with different digit. Hamming index from a graph is the number of Hamming distances between all pairs of strings. In this research, author discuss the Hamming index of graphs produced by an side-node incidence matrix, particularly windmill graph and snake graphs.