The competition index of two-colored non-hamiltonian digraph with two cycles whose lengths differ by three

4th International Conference on Operational Research

Sumardi, Hari^1 ; Suwilo, Saib^1 ; Rosmaini, Elly^1

Department of Mathematics, University of Sumatera Utara, Medan

20155, Indonesia^1

关键词: Colored digraphs;    Competition index;    Non-Hamiltonian;    Nonnegative integers;    Ordered pairs;    Positive integers;    Strongly connected;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/300/1/012075/pdf
DOI  :  10.1088/1757-899X/300/1/012075

来源: IOP

【 摘 要 】

A two-colored digraph is a digraph each of whose arcs is colored by red or blue. An (h, g)-walk in a two-colored digraph is a walk consisting of h red arcs and g blue arcs. A strongly connected two-colored digraph is primitive provided there exists a positive integer h + g such that for each ordered pair of vertices x and y there is a (h, g)-walk from x to y. The competition index of a primitive two-colored digraph is the least positive integer h + g over all pairs of nonnegative integers h and g such that for each pair of vertices x and y in there is a vertex w such that there are (h, g)-walks from x to w and from y to w. For some positive integer s ≥ 7 (s0 mod 3), we discuss the competition index of a class of strongly connected primitive two-colored digraph D(2)consisting of two cycles of lengths s and s + 3, respectively. We present the competition index of such primitive two-colored digraph D(2)in terms of s and the lengths of two specific paths in D(2).