Graceful labeling on a multiple-fan graph with pendants

A. Akerina, K. A. Sugeng

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

An injective function f from the set of vertices in a graph G to a set {0,1,?,n} is called graceful labeling if the function f induced the edge function f* from the set of edges of G to a set of positive integers {1,2,?,n} with f*(xy) = |f(x) - f(y)| for every edge xy ? E(G) such that every edge has a different label. A graph G that can be labeled with graceful labeling is called a graceful graph. The multiple-fan graph with k pendants F(n1,n2,?,nr),k is a graph obtained from r fan graphs Fni, with i = 1,2,?,r, which share the center vertex and then we add k pendants to the center vertex of the multiple-fan graph. In this paper, we show that the multiple-fan graph with k pendants is graceful, with ni = 2, i = 1,2,?, r and k = r - 1.

Original languageEnglish
Title of host publication3rd International Conference on Mathematics
Subtitle of host publicationEducation, Theory, and Application, ICMETA 2021
EditorsDiari Indriati, Tri Atmojo Kusmayadi, Sutrima Sutrima, Dewi Retno Sari Saputro, Putranto Hadi Utomo
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735440708
DOIs
Publication statusPublished - 8 Feb 2021
Event3rd International Conference on Mathematics: Education, Theory, and Application, ICMETA 2021 - Surakarta, Online, Indonesia
Duration: 20 Oct 2020 → …

Publication series

NameAIP Conference Proceedings
Volume2326
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference3rd International Conference on Mathematics: Education, Theory, and Application, ICMETA 2021
CountryIndonesia
CitySurakarta, Online
Period20/10/20 → …

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