On the Gracefulness of the Digraphs n·■_m
Feng Wei · Shuxue de shijian yu renshi · 2008
A digraph D(V,E) is said to be graceful if there exists an injection f:V(G)→{0,1,…,|E|} such that the induced function f′:E(G)→{1,2,…,|E|} which is defined by f′(u,v)={mod(|E|+1)) for every directed edge(u,v) is a bijection.Here,f is called a graceful labeling(graceful numbering) of D(V,E),and f′ is called the induced edge′s graceful labeling of D.In this paper we discuss the gracefulness of the digraph n·■m and prove that n·■m is a graceful digraph for m=23 and even n.