Analysis and computations of chromatic index for a class of integral sum graphs based on edge coloring and edge-sum coloring

Abstract

We consider families of integral sum graphs H−i,s m,ϕ and H−i,s ϕ,j , where −i < 0 < s, 1 ≤ m < i and 1 ≤ j < s for all i, s, m, j ∈ N. Since the graphs contains parameters i and s, so it is difficult to compute theoretical and numerical results. We apply edge coloring and edge-sum coloring on H−i,s ϕ,j and H−i,s m,ϕ . Here, we compute the general formula of chromatic index by considering the minimum number of independent color classes. Comparison between these two techniques can be done. Numerical results corroborate derived theoretical results.