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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Advanced Studies in Contemporary Mathematics Advanced Studies in Contemporary Mathematics Vol.31 No.2
- 발행연도
- 2021.4
- 수록면
- 205 - 210 (6page)
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초록· 키워드
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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.
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