Structure of Vertex Order on Almost Moore Digraphs with no Selfrepeat
Yus Mochamad Cholily · UMM Institutional Repository (University of Maine at Machias) · 2015
An almost Moore digraph, denoted by (d,k)-digraphs, is a diregular digraph of degree d > 1, diameter k > 1 and the number of vertices one less than the Moore bound. A vertex v is called repeat u, denoted by v = r(u) if there are two walks of lengths no more than k from u to v. Special case if u = fthen vertex u is called selfrepeat.The smallest positive integer p such that the composition rp(u) = u is called order of u. This study focuses on the digraphs with no selfrepeat. Especially, discussing on vertex orders of out-neighbor and in-neighbor of a vertex with smallest order.