On 1-vertex bimagic vertex labeling

Abstract

Abstract. A 1-vertex magic vertex labeling of a graph G with p vertices is defined as a bijection f from the vertices to the integers 1, 2, . . . , p with the property that there is a constant k such that at any vertex x,f (y) = k, where N (x) is the set of vertices adjacent to x. In this paper we introduce 1-vertex bimagic vertex labeling of a graph G and obtain the necessary condition for a graph to be 1-vertex bimagic. We exhibit the same type of labeling for some class of graphs and give some general results.

On 1-vertex bimagic vertex labeling

“…, |V ∪E |} is a vertex-magic total labeling if there is a constant k, called the magic constant, such that for every vertex v, f (v) + f (vu) = k where the sum is over all vertices u adjacent to v (some authors use the term "vertex-magic" for this concept). In [1,2], edge bimagic total labeling was introduced by J. Baskar Babujee. A graph G(p, q) with p vertices and q edges is called edge bimagic total if there exists a bijection f : V ∪ E → {1, 2, .…”

Edge magic and bimagic harmonious labeling of ladder graphs

“…In 1996, Ringel and Llado [3] called this labeling as edge magic. Edge bimagic labeling of graphs was introduced by Babujee [1] in 2004. Harmonious labeling naturally arose in the study by Graham and Sloane [4].…”

Encryption through labeled graphs using strong face bimagic labeling

“…In 2004 Babujee [2] introduced the notion of edge bimagic total labeling and also studied in [3] that a generalization of super edge magic total labeling in which there exists two distinct constants k 1 and k 2 such that the edge weights involved in this labeling are either equal to k 1 or k 2 . An edge bimagic labeling is of interest for graphs that do not have any super edge magic total labeling.…”