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All Journal ICMSA Abdimas Talenta : Jurnal Pengabdian Kepada Masyarakat
Saib Suwilo
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Agriculture, Biological Sciences & Forestry Law, Crime, Criminology & Criminal Justice Mathematics Social Sciences

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THE EXPONENT SET OF COMPLETE ASYMMETRIC 2-DIGRAPHS Saib Suwilo
Proceedings of ICMSA Vol 1, No 1 (2005): ICMSA 2005
Publisher : Proceedings of ICMSA

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Abstract

A 2-digraph is a digraph whose each ofits arcs is colored by either redor blue. The exponent ofa 2-digraphD is the smallest positive integerh + k over all possible nonnegative integers h and k such that for eachpair of vertices u and v in D there is a walk from u to v consisting of hred arcs and k blue arcs. In this paper, we show that for n 5 theexponent set of complete asymmetic 2-digraphs on n vertices is Eo :{2,3,4}.Keywords: 2-digraphs, primitive, exponent.
ON EXPONENTS OF PRIMITIVE GRAPHS Saib Suwilo
Proceedings of ICMSA Vol 1, No 1 (2005): ICMSA 2005
Publisher : Proceedings of ICMSA

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (3159.923 KB)

Abstract

A connected gaph G is primitive provided there exists a positive integerk such that for each pair of vertices u and v in G there is a walk of lengtht that connects u and v. The smallest of such positive integers k is calledthe exponent of G and is denoted by exp(G). In this paper, we give a newbound on exponent of primitive graphs G in terms of the length of thesmallest cycle of G. We show that the new bound is sharp andgeneralizes the bounds given by Shao and Liu et. al.Keywords: primitive graphs; exponents.
Co-Authors Elvina Herawati Mimmy Sari Syah Putri