A two-colored digraph D(2) is a digraph D whose each of its arc is colored by either red or blue. For nonnegative integers s and t with s+t > 0, an (s, t)-walk in a two-colored digraph is a walk of length s+t consisting of s red arcs and t blue arcs. The vector (s, t)T is the composition of the walk. A two-colored digraph D(2) is primitive provided that there exist nonnegative integers h and k such that for each pair of vertices u and v in D(2) there is an (h, k)-walk in D(2) from u to v. For a two-colored digraph consisting of two cycles D(2), we established a formula for the exponent of D(2) in terms of the compositions of its cycles and the compositions of two specified paths in D(2). We then apply the formula to the class of two-colored digraphs consisting of two cycles whose lengths differ by 1 and to the class of two-colored digraph consisting a cycle and a loop.
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22 May 2012
THE 5TH INTERNATIONAL CONFERENCE ON RESEARCH AND EDUCATION IN MATHEMATICS: ICREM5
22–24 October 2011
Bandung, Indonesia
Research Article|
May 22 2012
Exponents of two-colored digraphs consisting of two cycles
Saib Suwilo
Saib Suwilo
Department of Mathematics, University of Sumatera Utara,
Indonesia
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AIP Conf. Proc. 1450, 297–304 (2012)
Citation
Saib Suwilo; Exponents of two-colored digraphs consisting of two cycles. AIP Conf. Proc. 22 May 2012; 1450 (1): 297–304. https://doi.org/10.1063/1.4724158
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