The (1, 2)-step competition graph of a tournament
نویسندگان
چکیده
The competition graph of a digraph, introduced by Cohen in 1968, has been extensively studied. More recently, in 2000, Cho, Kim and Nam defined the m-step competition graph. Here, we offer another generalization of the competition graph. We define the (1,2)-step competition graph of a digraph D, denoted C1,2(D) , as the graph of V(D) where {x,y} is an element of E(C1,2(D)) if and only if there exists a vertex z ≠ x,y such that either dD-y(x,z) = 1 and dD-x(y,z) ≤ 2 or dD-x(y,z) = 1 and dD-y(x,z) ≤ 2. Here, we characterize the (1,2)-step competition graphs of tournaments and extend our results to the (i,k)-step competition graph of a tournament.
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ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 159 شماره
صفحات -
تاریخ انتشار 2011