Irregularity strength of dense graphs

Let G be a simple graph of order n with no isolated vertices and no isolated edges. For a positive integer w, an assignment f on G is a function f : E(G) {1, 2, . . . , w}. For a vertex v, f(v) is defined as the sum f(e) over all edges e of G incident with v. f is called irregular, if all f(v) are distinct. The smallest w for which there exists an irregular assignment on G is called the irregularity strength of G, and it is denoted by s(G). We show that if the minimum degree (G) 10n3/4 log1/4 n, then s(G) 48(n/)+6. For these , this improves the magnitude of the previous best upper bound of A. Frieze, R.J. Gould, M. Karo

• Type: Journal
• Year: 2008
• Where: JGT
• Authors: Bill Cuckler, Felix Lazebnik
• Keywords: Isolated Vertices, JGT 2008, Positive Integer, Simple Graph