Odd harmonious labeling on squid graph and double squid graph

F. Febriana, K. A. Sugeng

Research output: Contribution to journalConference articlepeer-review

2 Citations (Scopus)

Abstract

An injective function f from set of vertices in graph G to a set of {0,1,..,|E|-1} is called an odd harmonious labeling if the function f induced the edge function f∗ from the set of edges of G to a set of odd positive integer number {1,3,5,..,2|E|-1} with f∗(xy) = f(x) + f(y) for every edge xy in E. Graph that has an odd harmonious labeling is called odd harmonious graph. The squid graph Tn,k is a graph which is obtained from a cycle Cn and we add k pendant to one vertex of the cycle. It is known that Cn is an odd harmonious graph if and only if n = 0 mod 4. However, by adding at least one pendant in the cycle graph, we can label the new graph odd harmoniously for all even number of vertices. In this paper, we showed that the graph Tn,k and T2n,k are an odd harmonious graph, for n = 0 (mod 2), n ≥ 4 and k ≥ 1. The construction of the odd harmonious labeling of the graph Tn,k and T2n,k are inspired by the odd harmonious labeling of Cn for n = 0(mod 4).

Original languageEnglish
Article number012015
JournalJournal of Physics: Conference Series
Volume1538
Issue number1
DOIs
Publication statusPublished - 19 Jun 2020
Event3rd International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2019 - East Java, Indonesia
Duration: 26 Oct 201927 Oct 2019

Fingerprint

Dive into the research topics of 'Odd harmonious labeling on squid graph and double squid graph'. Together they form a unique fingerprint.

Cite this