On Non Inclusive Distance Vertex Irregularity Strength of Tadpole and Path Corona Path Graphs

Muhammad Bilal, Diari Indriati, Vika Yugi Kurniawan


Let 𝐺 = (𝑉, 𝐸) be a connected and simple graph with vertex set 𝑉(𝐺) and edge set
𝐸(𝐺). A non inclusive distance vertex irregular labeling of a graph 𝐺 is a mapping of πœ† ∢
(𝑉, 𝐺) β†’ {1, 2, … , π‘˜} such that the weights calculated for all vertices are distinct. The weight of a vertex 𝑣, under labeling πœ†, denoted by 𝑀𝑑(𝑣), is defined as the sum of the label of all vertices adjacent to 𝑣 (distance 1 from 𝑣). A non inclusive distance vertex irregularity strength of graph 𝐺, denoted by 𝑑𝑖𝑠(𝐺), is the minimum value of the largest label π‘˜ over all such non inclusive distance vertex irregular labeling. In this research, we determined 𝑑𝑖𝑠(𝐺) from π‘‡π‘š,𝑛 graph with π‘š β‰₯ 3, π‘š odd, π‘Žπ‘›π‘‘ 𝑛 β‰₯ 1 and 𝑃𝑛 βŠ™ 𝑃𝑛 graph π‘€π‘–π‘‘β„Ž 𝑛 β‰₯ 2 and 𝑛 even.


non inclusive distance irregular labeling, non inclusive distance vertex irregularity strength, tadpole graph, path corona path graph


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