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Odd harmonious labeling of two graphs containing star

机译:奇怪的和谐标记包含星的两个图表

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An odd harmonious labeling of a graph G is an injective function f:V(G)→{0,1,2,...,2|E(G)|-1} such that the induced function f~*:E(G)→{1,3,...,2|E(G)|-1} defined by f~*(xy)=f(x)+f(y) is a bijection. A graph that admits odd harmonious labeling is called an odd harmonious graph. The concept of odd harmonious labeling was initiated by Liang and Bai in 2009. By the result of Liang and Bai, a star is an odd harmonious graph. Motivated by a result, we prove that two graphs containing star are still odd harmonious. In this case, we prove that a double stars is an odd harmonious graph. The remaining we prove that an even cycle and a star which is sharing a common vertex is also an odd harmonious graph.
机译:图G的奇怪和谐标记是注射功能F:V(g)→{0,1,2,...,2 | e(g)| -1},使得诱导的功能f〜*:e (g)→{1,3,......,2 | e(g)| -1}由f〜*(xy)= f(x)+ f(y)是一个自呼口。 承认奇怪的和谐标签的图表称为奇怪的和谐图。 2009年梁和白王和白湾发起了奇怪和谐标签的概念。通过梁和白,一颗星是一个奇怪的和谐图。 由于结果,我们证明了一个包含明星的两个图仍然是奇怪的和谐。 在这种情况下,我们证明了双星是一个奇怪的和谐图。 剩下的我们证明了一个偶数周期和共享共同点的星星也是一个奇怪的和谐图。

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