Abstract

Graph labelling is an interesting and fast developing branch in graph theory. Graph labelling applications include genomics, electrical engineering, operations research, transcriptome analysis, Golomb rulers etc. In this paper, Arithmetic number labelling induced from arithmetic numbers of some standard graphs namely path, cycle, bull graph, star graph, bistar graph, jelly fish graph, tadpole graph and tree were studied. In this paper, Arithmetic number labelling of subdivided star graph S (K_{1, n}) and union of two subdivided star graphs S (K_{1, n}) È  S (K_{1, m}), union of subdivided star graph with star graph S (K_{1, n}) È K_{1, m}, union of subdivided star graph with bistar graph S (K, n) È B r, s are studied. Also, Python program code to generate the vertex labels of the union of subdivided star graph and bistar graph S (K, n) È B r, s is given. Appropriate examples are given.

Keywords — Arithmetic number, Arithmetic number labelling, Subdivided star graph, Union Graph.