Antimagic labeling of n-uniform cactus chain graphs

Title

Antimagic labeling of n-uniform cactus chain graphs

Creator

Joseph, Ancy Kandathil; Kureethara, Joseph Varghese

Description

A graph G = (V,E) is considered antimagic if it admits antimagic labeling. The antimagic labeling of a finite, simple graph with |V | = n and |E| = m is a bijective function from the set of edges to the set of integers {1, 2,,m} such that the vertex sum of n vertices is pairwise distinct. The vertex sum of a vertex is obtained by summing the labels of all edges incident to it. Hartsfield and Ringel conjectured that every connected graph different from K2 is antimagic. Supporting this conjecture, it was shown that the dense graphs are antimagic. A cactus graph is a connected graph where no edge lies within more than one cycle. A cactus graph in which each block is a cycle of the same size n is called an n-uniform cactus graph. We proved that Hartsfield and Ringels conjecture is true for n-uniform cactus chain graphs with and without pendant vertices, which are specific cases of sparse graphs. 2026 World Scientific Publishing Company.

Source

Discrete Mathematics, Algorithms and Applications;Volume;18;Issue;1;Article No.;2550015;

Date

01-01-2026

Publisher

World Scientific

Subject

antimagic labeling; cactus chain graph; equivalence class; Graph labeling

Coverage

Joseph A.K., Department of Mathematics, Christ University, Bangalore, 560029, India; Kureethara J.V., Department of Mathematics, Christ University, Bangalore, 560029, India

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 17938309;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793830925500156

https://www.scopus.com/pages/publications/85217639314?origin=resultslist