Proper Colourings in r -Regular Inverse Sum Indeg Index Graphs - E. Litta; S. Narmadha (Research and Applications Towards Mathematics and Computer Science Vol. 9, 2024)
Let G(V,E) be a simple undirected graph. The Inverse sum indeg index of a graph G is defined as ISI(G) = _r,sE(G) drds dr + ds where ds is the degree of the vertex s in G. The new idea of proper colourings in the Inverse sum indeg index graph has been proposed in this chapter. Some families of graphs such as cycle, generalized Petersen graph and complete graph which satisfies the condition of r–regular Inverse sum indeg index. The inequalities for the chromatic number related to Inverse sum indeg index are developed.