2012/07/12 by Sin-Min Lee, Saeid Alikhani, Lee, Sin-Min +5
Mathematics · #05C25 #05C78 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C25 #msc:05C78
paper · pdf · doi:10.48550/arxiv.1207.2977
arxiv created 2012/07/13 · arxiv updated 2012/07/16
Let G be a graph with vertex set V and edge set E such that |V| = p and |E| = q. For integers k≥ 0, define an edge labeling f : E → \k,k+1,....,k+q-1\ and define the vertex sum for a vertex v as the sum of the labels of the edges incident to v. If such an edge labeling induces a vertex labeling in which every vertex has a constant vertex sum (mod p), then G is said to be k-edge magic (k-EM). In this paper, we (i) show that all the maximal outerplanar graphs of order p = 4; 5; 7 are k-EM if and only if k≡ 2 (mod p); (ii) obtain all the maximal outerplanar graphs that are k-EM for k = 3; 4; and (iii) characterize all (p; p-h)-graph that are k-EM for h≥ 0. We conjecture that all maximal outerplanar graphs of prime order p are k-EM if and only if k ≡ 2 (mod p).