Odd harmonious labeling on squid graph and double squid graph
F Febriana, Kiki Ariyanti Sugeng · Journal of Physics Conference Series · 2020
Abstract An injective functionffrom set of vertices in graphGto a set of {0,1,…,|E| − 1} is called an odd harmonious labeling if the functionfinduced the edge functionf* from the set of edges ofGto a set of odd positive integer number {1,3,5,…,2|E| − 1} withf*(xy) =f(x) +f(y) for every edgexyinE.Graph that has an odd harmonious labeling is called odd harmonious graph. The squid graphTn,kis a graph which is obtained from a cycleCnand we addkpendant to one vertex of the cycle. It is known thatCnis an odd harmonious graph if and only ifn= 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 graphTn,kandT2n,kare an odd harmonious graph, forn= 0 (mod 2),n≥ 4 andk≥ 1. The construction of the odd harmonious labeling of the graphTn,kandT2n,kare inspired by the odd harmonious labeling ofCnforn= 0(mod 4).