A Study on Adjacent Vertex Distinguish Proper Edge Coloring for Families of Integral Sum Graphs

Abstract

Here, we consider families of integral sum graphs G−r,s, H−r,s, H−r,s and H−r,s where −r < 0 < s, 1 ≤ i < r and 1 ≤ j < s for all i, s, r, j ∈ N. We apply edge coloring so that any pair of adjacent vertices are not getting same set of colors. We derive the AVD proper edge chromatic number for the families of integral sum graphs. To support theoretical findings, we present numerical results. The study of graph coloring associated with integral sum graphs can be used to exchange confidential information, make a schedule, store and manipulate relational computer data bases, and operate networking, etc.