应用数学学报 2013, Vol. 36 Issue (6): 1037-1043    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索  |  1. 山西大学数学科学学院, 太原 030006;
2. 太原科技大学应用数学系, 太原 030024
The (i, k)-step Competition Graph of a Round Digraph
ZHANG Xinhong1,2, LI Ruijuan1, LI Shengjia1
1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006;
2. Department of Applied Mathematics, Taiyuan University of Science and Technology, Taiyuan 030024
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Abstract： The competition graph of a digraph, created by Cohen for studying a biological model in 1968, has been extensively studied. In 2011, Factor et al. defined the (i, k)-step competition graph of a digraph D, denoted C1,2(D), as the graph on V(D) where {x, y}∈E(C1,2(D)) if and only if there exists a vertex zx, y, such that either dD-y(x, z)≤i and dD-x(y, z)≤k or dD-x(y, z)≤i and dD-x(x, z)≤k. In this paper, the (i, k)-step competition graph Ci, k(D) of a round-digraph D is characterized and a sufficient and necessary condition for any two vertices in D to be adjacent in Ci, k(D) is given in the paper.

 引用本文: 张新鸿,李瑞娟,李胜家. 圆有向图的(i,k)步竞争图[J]. 应用数学学报, 2013, 36(6): 1037-1043. ZHANG Xinhong,LI Ruijuan,LI Shengjia. The (i, k)-step Competition Graph of a Round Digraph[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(6): 1037-1043.

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