## 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 T_{n,k} is a graph which is obtained from a cycle C_{n} and we add k pendant to one vertex of the cycle. It is known that C_{n} 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 T_{n,k} and T_{2n,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 T_{n,k} and T_{2n,k} are inspired by the odd harmonious labeling of C_{n} for n = 0(mod 4).

Original language | English |
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Article number | 012015 |

Journal | Journal of Physics: Conference Series |

Volume | 1538 |

Issue number | 1 |

DOIs | |

Publication status | Published - 19 Jun 2020 |

Event | 3rd International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2019 - East Java, Indonesia Duration: 26 Oct 2019 → 27 Oct 2019 |