Hamming index of graphs with respect to its incidence matrix

Harishchandra S. Ramane (Karnatak University, Dharwad)
Ishwar B. Baidari (Karnatak University, Dharwad)
Raju B. Jummannaver (Karnatak University, Dharwad)
Vinayak V. Manjalapur (Karnatak University, Dharwad)
Gouramma A. Gudodagi (Karnatak University, Dharwad)
Ashwini S. Yalnaik (Karnatak University, Dharwad)
Ajith S. Hanagawadimath (Karnatak University, Dharwad)

Indonesian Journal of Combinatorics
Vol 6, No 2 (2022)

Let B(G) be the incidence matrix of a graph G. The row in B(G)corresponding to a vertex v, denoted by s(v) is the string which belongs to ℤm2, a set of m-tuples over a field of order two. The Hamming distance between the strings s(u) and s(v) is the number of positions in which s(u) and s(v) differ. In this paper we obtain the Hamming distance between the strings generated by the incidence matrix of a graph. The sum of Hamming distances between all pairs of strings, called Hamming index of a graph is obtained.