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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Kiki A. Sugeng
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok, Indonesia, and Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia
Electrical & Electronics Engineering

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Graceful labeling construction for some special tree graph using adjacency matrix Nikson Simarmata; Ikhlas Pratama Sandy; Kiki A. Sugeng
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.1

Abstract

In 1967, Rosa introduced β − labeling which was then popularized by Golomb under the name graceful. Graceful labeling on a graph G is an injective function f : V(G)→{0, 1, 2, …, |E(G)|} such that, when each edge uv ∈ E(G) is assigned the label |f(u)−f(v)| the resulting edge labels are distinct. If graph G has graceful labeling then G is called a graceful graph. Rosa also introduced α − labeling on graph G which is a graceful labeling f with an additional condition that there is λ ∈ {1, 2, …, |E(G)|} so that for every edge uv ∈ E(G) where f(u)<f(v) then f(u)≤λ < f(v). This paper gives a new approach to showing a graph is admitted α − labeling using an adjacency matrix. Then this construction will be used to construct graceful labeling for the superstar graph. Moreover, we give a graceful labeling construction for a super-rooted tree graph.
Co-Authors Ikhlas Pratama Sandy Nikson Simarmata