Integral sum graphs Gn and G-r,n are perfect graphs - Julia K. Abraham; Sajidha P.; Lowell W. Beineke; Vilfred V.; L. Mary Florida (AKCE International Journal of Graphs and Combinatorics, 2024)
AbstractA graph G is an integral sum graph (sum graph) if its vertices can be labeled with distinct integers (positive integers) so that e = uv is an edge of G if and only if the sum of the labels on vertices u and v is also a label in G. A graph G is perfect if the chromatic number of each of its induced subgraphs is equal to the clique number of the same. A simple graph G is of class 1 if its edge chromatic number and maximum degree are same. In this paper, we prove that integral sum graphs Gn, [Formula: see text] and [Formula: see text] over the label sets [Formula: see text] and [Formula: see text], respectively, are perfect graphs as well as of class 1 for [Formula: see text]. We also obtain a few structural properties of these graphs.