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For a positive integer m and a digraph D, them-step com-petition graph Cm (D) of D has the same set of vertices as D and an edge between vertices u and v if and only if there is a vertexx in D such thatthere are directed walks of lengthm from u to x and from v to x. Choand Kim [6] introduced notions of competition index and competitionperiod of D for a strongly connected digraph D. In this paper, we extendthese notions to a general digraph D. In addition, we study competitionindices of tournaments.
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참고문헌 (18)
참고문헌 신청
B. Liu / 2000 / Matrices in Combinatorics and Graph Theory / Kluwer Academic Publishers
B. R. Heap / 1966 / The structure of powers of nonnegative matrices / SIAM J. Appl. Math 14 : 610 ~ 640
B. Zhou / 2002 / On generalized exponents of tournaments / Taiwanese J. Math 6 : 565 ~ 572
H. H. Cho / 1993 / Indices of irreducible Boolean matrix / J. Korean Math. Soc 30 : 78 ~ 85
H. H. Cho / 2000 / The m-step competition graph of a digraph / Discrete Appl. Math 105 : 115 ~ 127
B. R. Heap / 1966 / The structure of powers of nonnegative matrices / SIAM J. Appl. Math 14 : 610 ~ 640
B. Zhou / 2002 / On generalized exponents of tournaments / Taiwanese J. Math 6 : 565 ~ 572
H. H. Cho / 1993 / Indices of irreducible Boolean matrix / J. Korean Math. Soc 30 : 78 ~ 85
H. H. Cho / 2000 / The m-step competition graph of a digraph / Discrete Appl. Math 105 : 115 ~ 127
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