## Some New Results on Set-Graceful and Set-Sequential Graphs

Publication Type : Journal Article

Publisher : Journal of Combinatorics System Sciences

Source : Journal of Combinatorics & System Sciences, Volume 37, Issue 2-4, p.229 (2012)

Accession Number : 89895993

Campus : Coimbatore

School : School of Engineering

Department : Mathematics

Verified : Yes

Year : 2012

Abstract : pA set-indexer of a given graph G = (V, E) is an assignment f of distinct nonempty subsets of a finite nonempty 'ground set' X = {x1, x2,...,xn} of car dinality n, where 2X denotes the power set of X, to the vertices of G so that the values f âŠ•(e), e = uv âˆˆ E; obtained as the symmetric differences f(u) âŠ• f(v) of the subsets f(u) and f(v) of X, are all distinct. It is well known that every graph admits a set-indexer. A function f : Vâˆª E â†’ Y = 2X â€“ {âˆ…} is called a set-sequential labeling of G = (V, E) if it is a bijection and for all uv âˆˆE, f(u) âŠ• f(v) = f(uv): A graph is called set-sequential if it admits a set-sequential labeling. A set-indexer f of a graph G = (V, E) is called a set-graceful labeling of G if there exists a nonempty ground set X such that fâŠ•(E) = 2X âˆ’ {âˆ…} and G is setgraceful if it admits a set-graceful labeling. In this article we provide characterization of m copies of K2 , mK2 , that are set-sequential and the friendship graphs C3m, consisting of m triangles attached at one common vertex that are set-graceful. It is also established that for every set X of odd cardinality there is a set-sequential tree of diameter four./p

Cite this Research Publication : B. D. Acharya, Germina, K. A., Abhishek, K., and Slater, P. J., “Some New Results on Set-Graceful and Set-Sequential Graphs”, Journal of Combinatorics & System Sciences, vol. 37, no. 2-4, p. 229, 2012.