TY - GEN

T1 - Graceful labeling on a multiple-fan graph with pendants

AU - Akerina, A.

AU - Sugeng, K. A.

N1 - Funding Information:
This research is funded by UI Research Grant No. NKB-2412/UN2.RST/HKP.05.00/2020.
Publisher Copyright:
© 2021 Author(s).
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2/8

Y1 - 2021/2/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85101652874&partnerID=8YFLogxK

U2 - 10.1063/5.0039411

DO - 10.1063/5.0039411

M3 - Conference contribution

AN - SCOPUS:85101652874

T3 - AIP Conference Proceedings

BT - 3rd International Conference on Mathematics

A2 - Indriati, Diari

A2 - Kusmayadi, Tri Atmojo

A2 - Sutrima, Sutrima

A2 - Saputro, Dewi Retno Sari

A2 - Utomo, Putranto Hadi

PB - American Institute of Physics Inc.

T2 - 3rd International Conference on Mathematics: Education, Theory, and Application, ICMETA 2021

Y2 - 20 October 2020

ER -