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The (1,2)-Step Competition Graph of a Tournament by Kim A.S. Factor; Sarah K. Merz is a Computer Science article available to read on EtoBox.
What is The (1,2)-Step Competition Graph of a Tournament about?
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. In this paper, we offer another generalization of the competition graph. We define the (1, 2)-step competition graph of a digraph D, denoted C 1,2 (D), as the graph on V (D) where {x, y} ∈ E(C 1,2 (D)) if and only if there exists a vertex z ̸ = x, y, such that either d D-y (x, z) = 1 and d D-x (y, z) ≤ 2 or d D-x (y, z) = 1 and d D-y (x, z) ≤ 2. In this paper, we characterize the (1, 2)-step competition graphs of tournaments and extend our results to the (i, k)-step competition graph of a tournament.
Who reads The (1,2)-Step Competition Graph of a Tournament?
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- Author
- Kim A.S. Factor; Sarah K. Merz
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-218X)
- Published
- 2011
- Language
- EN
- Field
- Computer Science (Physical Sciences)