Year: 2025
Type: article
Abstract: We introduce the notion of total distance irregular labeling, called the local total distance irregular labeling. All edges and vertices are labeled with positive integers 1 to k such that the weight calculated at the vertices induces a vertex coloring if two adjacent vertices has different weight. The weight of a vertex $u\in V(G)$ is defined as the sum of the labels of all vertices adjacent and edges incident to $u$ (distance $1$ from $u$). The minimum cardinality of the largest label over all such irregular assignment is called the local total distance irregularity strength, denoted by $tdis_l(G)$. In this paper, we established the lower bound of the local total distance irregularity strength of graphs $G$ and determined exact values of some classes of graphs namely path, cycle, star, bipartite complete, fan and sun graph.
Authors: Eric Dwi Putra, Slamin, Arika Indah Kristiana, Abi Suwito, Ridho Alfarisi
Institutions: Universitas Jember, Universitas PGRI Argopuro Jember
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: Universitas Jember
OpenAlex ID: W7111056141
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