ANALYSIS AND COMPUTATIONS OF CHROMATIC INDEX FOR A CLASS OF INTEGRAL SUM GRAPHS BASED ON EDGE COLORING AND EDGE-SUMCOLORING

ANALYSIS AND COMPUTATIONS OF CHROMATIC INDEX FOR A CLASS OF INTEGRAL SUM GRAPHS BASED ON EDGE COLORING AND EDGE-SUMCOLORING

B. R. Priyanka, B. Pandit, M. Rajeshwari, R. P. Agarwal

[PDF]

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.

Keywords

Edge coloring, edge sum coloring, integral sum graph, graph coloring.