2-Eksponen Digraph Dwiwarna Asimetrik dengan Dua Cycle yang Bersinggungan

Abstract

Let D be a asymmetric two-colored digraph on n = 2m, m 4 vertices which have a common vertex and the length of each cycles is m and m + 1. Since D is asymmetric, there exists two cycles of length m are denoted by γ1 and γ2 and two cycles of length m + 1 are denoted by γ3 and γ4 and also has cycles of length 2. If γ1 dan γ3 have each exactly one blue arc, This research will show that usedly a 2 by 2 submatrix with determinant 1 of cycle matrix in D then obtained exp2(D) ≤ 1 (2n2 − n − 6). On emprical data show that the 2-exponents of D can be achieved using (h, k)-walks with h = k. Using this fact we show that exp2(D) ≤ (n +2n).