Magical coronations of graphs
Ramón M. Figueroa-Centeno, Rikio Ichishima, Francesc Antoni Muntaner-Batle · 2002
A(p, q) graphGis called edge-magic if there exists a bijective function f: V (G) ∪ E(G) →{1, 2,...,p+ q} such that f(u) +f(v) +f(uv) is constant for any edge uv of G. Moreover, G is said to be super edgemagic if f(V (G)) = {1, 2,...,p}. Every super edge-magic (p, q) graph is harmonious, sequential and felicitous whenever it is a tree or satisfies q ≥ p. In this paper, we prove that the n-crown, a cycle with n pendant edges attached at each vertex, is super edge-magic for any positive integer n, and thus extend what was known about the harmoniousness, sequentialness and felicitousness of such graphs. We also present three results on attaching pendant edges to the vertices of certain super edge-magic graphs to obtain more super edge-magic graphs. Dedicated to Tadashi Iida