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ON HARMONIOUS COLORINGS OF LEXICOGRAPHIC PRODUCT OF GRAPHS
K. KALIRAJ,M. MANJULA,VERNOLD VIVIN,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.2
Harmonious coloring was rst introduced by Harary and Plantholt in 1982. A harmonious coloring is a proper vertex coloring in which every pair of colors appears on at most one pair of adjacent vertices. The harmonious chromatic number χH(G) of a graph G is the minimum number of colors needed for any harmonious coloring of G. In this paper, we obtain the harmonious chromatic number of lexicographic product of two graphs G and H, denoted by G[H]. Path and complete graphs are used to obtain extremal properties of graphs and to obtain upper and lower bounds for some graph parameters. Here, we rst consider the graph G[H] where G is the complete graph and H is any simple graph such as the path graph, cycle graph, wheel graph, complete graph, star graph, fan graph or complete bipartite graph. Secondly, we consider G as the path graph and H as the complete graph or path graph respectively. Finally, we consider G as the wheel graph and H as the complete graph.
On r-dynamic coloring of n-Sunlet graph families
G. Nandini,M. Venkatachalam,Vernold Vivin. J.,Dafik 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.1
On r-dynamic coloring of n-Sunlet graph families