The sum of hamming distance for some composite graphs relative to vertex-edge incidence matrix

Abstract

Given C be a vertex-edge incidence matrix of a graph Z. The Hamming distance between two rows C(x, :) and C(y, :) of C is the number of coloumn ℓ such that C (x, ℓ) ≠ C (y, ℓ). In this paper, we discuss the sum of Hamming distances between all pairs of rows of C. We present a formula for the sum of the number of edges and the number of vertices of the graph Z. We then use this formula to determine the sum of Hamming distance for composite graphs such as union of graphs, joint of graphs, corona product of graphs and cartesian product of graphs