Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2009-10-01

Journal: ARS COMBINATORIA

Included Journals: SCIE

Volume: 93

Page Number: 431-438

ISSN: 0381-7032

Key Words: book graph; super edge-magic labeling; vertex labeling; edge labeling

Abstract: A graph G is called super edge-magic if there exists a bijection f from V(G) boolean OR E(G) to {1, 2,..., vertical bar V(G)vertical bar + vertical bar E(G)vertical bar} such that f(u) + f(nu) + f(u nu) = C is a constant for any u nu is an element of E(G) and f(V(G)) = {1, 2,..., vertical bar V(G)vertical bar}, f(E(G)) = {vertical bar V(G)vertical bar + 1, vertical bar V(G)vertical bar + 2,..., vertical bar V(G)vertical bar + vertical bar E(G)vertical bar}. R. M Figueroa-Centeno et al. provided the following conjecture: For every integer n >= 5, the book B-n is super edge-magic if and only if n is even or n equivalent to 5(mod 8). In this paper, we show that B-n is super edge-magic for even n >= 6.