Upper bounds on inclusive distance vertex irregularity strength
An inclusive distance vertex irregular labeling of a graph $G$ is an assignment of positive integers \(\{1,2,3,\dots,k\}\) to the vertices of $G$ such that for every vertex the sum of numbers assigned to its closed neighborhood is different. The minimum number $k$ for which an inclusive distance vertex irregular labeling of $G$ exists is denoted by $(\text{dis})(G)$. In this paper, the authors find some upper bounds of $(\text{dis})(G)$ for any distinct vertices of a graph $G$ and also for the forest and spider graph and finish the paper with a conjecture on trees for further research.
scientific article; zbMATH DE number 7435751