Achromatic Index of Unitary Addition Cayley Graph
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Abstract
For a positive integer n >1, the unitary addition Cayley Graph Gn = Cay+ (Zn ,Un) is the graph whose vertex set is Zn and if Un = {a E Zn : gcd(a,n) = 1} , Zn the integers modulo n then two vertices a,b are adjacent if and only if a+b E Un. In this research, we study about the unitary addition Cayley graphs, Gn = Cay+ (Zn ,Un), and to find the lower bound and upper bound of achromatic index of unitary addition Cayley graph where n is even and we improve the bound of achromatic index of graph Gn when n=2k , k is the positive integer. Moreover, we found that the unitary addition Cayley graph Gn is the complete bipartite graph K2k-1,2k-1 for n=2k.
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References
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