On Equitable Irregular Graphs
International Journal of Recent Technology and Engineering (IJRTE) ยท 2020
An kโedge-weighting of a graph G = (V,E) is a map ๐: ๐ฌ(๐ฎ) โ {๐,๐,๐, . . . ๐}, }where ๐ โฅ ๐ is an integer. Denote ๐บ๐(๐) is the sum of edge-weights appearing on the edges incident at the vertex v under๐ . An k-edge -weighting of G is equitable irregular if |๐บ๐(๐) โ ๐บ๐(๐)| โค ๐, for every pair of adjacent vertices u and v in G. The equitable irregular strength ๐บ๐ (๐ฎ) of an equitable irregular graph G is the smallest positive integer k such that there is a k-edge weighting of G. In this paper, we discuss the equitable irregular edge-weighting for some classes of graphs