On The Super Edge-Magic Deficiency Of Graphs.
Ramón M. Figueroa-Centeno, Rikio Ichishima, Francesc Antoni Muntaner-Batle · Ars Combinatoria · 2006
Abstract A (p, q) graph G is 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 ) = k is a constant, called the valence of f , for any edge uv of G . Moreover, G is said to be super edge-magic if f ( V ( G )) = {1,2,…, p }. The question studied in this paper is for which graphs is it possible to add a finite number of isolated vertices so that the resulting graph is super edge-magic? If it is possible for a given graph G , then we say that the minimum such number of isolated vertices is the super edge-magic deficiency, μ s (G) of G ; otherwise we define it to be + ∞.