On k-Super Graceful Labeling of Graphs

Publication Date

1-1-2022

Document Type

Article

Publication Title

Thai Journal of Mathematics

Volume

20

Issue

3

First Page

1375

Last Page

1387

Abstract

Let G = (V (G), E(G)) be a simple, finite and undirected graph of order p and size q. For k ≥ 1, a bijection f: V (G) ∪ E(G) → {k, k + 1, k + 2, …, k + p + q − 1} such that f(uv) = |f(u) − f(v)| for every edge uv ∈ E(G) is said to be a k-super graceful labeling of G. We say G is k-super graceful if it admits a k-super graceful labeling. In this paper, we study the k-super gracefulness of some standard graphs. Some general properties are obtained. Particularly, we found many sufficient conditions on k-super gracefulness for many families of (complete) bipartite and tripartite graphs. We show that some of the conditions are also necessary.

Keywords

bipartite and tripartite graphs, graceful labeling, k-super graceful labeling

Department

Mathematics and Statistics

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