On Non Inclusive Distance Vertex Irregularity Strength of Tadpole and Path Corona Path Graphs
Muhammad Bilal, Diari Indriati, Vika Yugi Kurniawan ยท Journal of Mathematics and Mathematics Education ยท 2020
Let ๐บ = (๐, ๐ธ) be a connected and simple graph with vertex set ๐(๐บ) and edge set ๐ธ(๐บ). A non inclusive distance vertex irregular labeling of a graph ๐บ is a mapping of ๐ โถ (๐, ๐บ) โ {1, 2, โฆ , ๐} such that the weights calculated for all vertices are distinct. The weight of a vertex ๐ฃ, under labeling ๐, denoted by ๐ค๐ก(๐ฃ), is defined as the sum of the label of all vertices adjacent to ๐ฃ (distance 1 from ๐ฃ). A non inclusive distance vertex irregularity strength of graph ๐บ, denoted by ๐๐๐ (๐บ), is the minimum value of the largest label ๐ over all such non inclusive distance vertex irregular labeling. In this research, we determined ๐๐๐ (๐บ) from ๐๐,๐ graph with ๐ โฅ 3, ๐ odd, ๐๐๐ ๐ โฅ 1 and ๐๐ โ ๐๐ graph ๐ค๐๐กโ ๐ โฅ 2 and ๐ even.