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    On the dot product of graphs over monogenic semigroups
    (Elsevier Science Inc, 2018) Akgunes, Nihat; Cagan, Busra
    Now define S a cartesian product of finite times with S-M(n) which is a finite semigroup having elements {0, x, x(2),..., x(n)} of order n. Gamma(S) is an undirected graph whose vertices are the nonzero elements of S. It is a new graph type which is the dot product. k be finite positive integer for 0 <={i(t)}(t=1)(k), {j(t)}(t=1)(k) <= n, any two distinct vertices of S (x(i1), x(i2),..., x(ik)) and (x(j1), x(j2),..., x(jk)) are adjacent if and only (x(i1), x(i2),..., x(ik)) . (x(j1), x(j2),..., x(jk))=0(SMn) (under the dot product) and it is assumed x(it) =0(SMn) if i(t)=0. In this study, the value of diameter, girth, maximum and minimum degrees, domination number, clique and chromatic numbers and in parallel with perfectness of Gamma(S) are elucidated. (C) 2017 Elsevier Inc. All rights reserved.