ACYCLIC DIGRAPHS WHOSE 2-STEP COMPETITION GRAPHS ARE P$P_n\cup\ I_2$

• Cho, Han-Hyun (Department of Mathematics Education, Seoul National University) ;
• Kim, Suh-Ryung (Department of Mathematics, Kyung Hee University) ;
• Nam, Yunsun (Department of Mathematics, Ewha Women’s University)
• 발행 : 2000.11.01

초록

The 2-step competition graph of D has the same vertex set as D and an edge between vertices x and y if and only if there exist (x, z)-walk of length 2 and (y, z)-walk of length 2 for some vertex z in D. The 2-step competition number of a graph G is the smallest number k such that G together with k isolated vertices is the 2-step competition graph of an acyclic digraph. Cho, et al. showed that the 2-step competition number of a path of length at least two is two. In this paper, we characterize all the minimal acyclic digraphs whose 2-step competition graphs are paths of length n with two isolated vertices and construct all such digraphs.

참고문헌

1. Congr. Numer. v.100 New Classes of p-Competition Graphs and φ-Tolerance Competition Graphs C. A. Anderson;L. Langley;J. R. Lundgren;P. A. McKenna;S. K. Merz
2. Graph Theory with Applications J. A. Bondy;U. S. R. Murty
3. Discrete Appl. Math. v.23 Niche Graphs C. Cable;K. F. Johns;J. R. Lundgren;S. Seager
4. Congr. Number. v.123 A Sufficient Condition for a Tree Belonging to T(2, 2, n) H. H. Cho;S-R. Kim;Y. Nam
5. To appear in Discrete Applied Mathematics The m-Step Competition Graphe of a Digraph H. H. Cho;S-R. Kim;Y. Nam
6. manuscript A Characterization of the Trees whose 2-Step Competition Numbers Are Two H. H. Cho;S-R. Kim;Y. Nam
7. Document 17696-PR Interval Graphs and Food Webs: A Finding and a Problem J. E. Cohen
8. Competition Graphs and Scientific Laws for Food Webs and Other Systems S-R. Kim
9. Quo Vadis, Graph Theory?, Annals of Discrete Mathematics v.55 The competition Number and Its Variants S-R. Kim;J. Gimbel(ed.);J. W. Kennedy(ed.);L. V. Quintas(ed.)
10. Discrete Applied Math. v.46 p-Competition Numbers S-R. Kim;T. McKee;F. R. McMorris;F. S. Roberts
11. Linear Algebra and Its Applications v.217 p-Competition Graphs S-R. Kim;T. McKee;F. R. McMorris;F. S. Roberts
12. Applications of Combinatorics and Graph Theory to the Biological and Social Sciences, IMH Volumes in Mathematics and Its Application v.17 Food Webs, Competition Graphs, Competition-Common Enermy Graphs, and Niche Graphs J. R. Lundgren;F. S. Roberts(ed.)
13. Graphs and Applications: Proceedings of the First Colorado Symposium of Graph Theory Food Webs with Interval Competition Graphs J. R. Lundgren;J. S. Maybee
14. Methods of Operations Research v.47 Generalized Competition Graphs and their Applications A. Raychaudhuri;F. S. Roberts;P. Brucher(ed.);R. Pauly(ed.)
15. Theory and Applications of Graphs Food Webs, Competition Graphs, and the boxicity of Ecological Phase Space F. S. Roberts;Y. Alavi(ed.);D. Lick(ed.)
16. Discrete Appl. Math. v.17 The Competition-Common Enemy Graph of a Digraph D. Scott
17. Proc. Symp. Appl. Math. Amer. Math. Soc. Providence v.30 Graph Theory, Homology, and Food Webs, in Population Biology G. Sugihara;S. A. Levin(ed.)
18. Competition Graphs, Threshold Graphs and Threshould Boolean Functions C. Wang