On the Minimum Span of Cone, Tadpole, and Barbell Graphs

Hafif Komarullah, Ikhsanul Halikin, Kiswara Agung Santoso Β· Advances in computer science research Β· 2022

Let 𝐺 be a simple and connected graph with 𝑝 vertices and π‘ž edges.An 𝐿(2,1)-labelling on the graph 𝐺 is a function 𝑓: 𝑉(𝐺) β†’ {0, 1, … , π‘˜} such that every two vertices with a distance one receive labels that differ by at least two, and every two vertices at distance two receive labels that differ by at least one.A number π‘˜ is called as span of 𝐿(2.1)labelling, if π‘˜ is the largest vertex labels.The span of a graph 𝐺 can be more than one, the minimum value of the span of a graph 𝐺 is notated by πœ† (2,1) (𝐺).In this paper, we determine the minimum span of cone, tadpole, and barbell graphs

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