Work

Exploring sigma coloring within lexicographic products of innovative graph families

Year: 2026

Type: article

Abstract: Sigma coloring is a vertex coloring strategy that distinguishes adjacent vertices by the sum of colors in their open neighborhood. The minimum number of colors needed in a sigma coloring of a graph $G$ is called its sigma chromatic number $\sigma\left(G\right)$. The bounds of $\sigma\left(G\right)$ are sharp. For every graph $G$, $\sigma\left(G\right)\leq\chi\left(G\right)$. In this article, a clear investigation is made under sigma coloring on the lexicographic product of a path graph with various graph families including path, cycle, star, double star, and comb graphs. Additionally, the sigma chromatic number for each case is found and verified with chromatic number for bounds.

Source: Statistics Optimization & Information Computing

DOI: 10.19139/soic-2310-5070-3306

Authors: Mohanapriya Nagaraj, Divya Senathipathy, Rinurwati, Robiatul Adawiyah, Ririana Annisatul Lathifah

Institutions: Kongunadu Arts and Science College, Institut Teknologi Sepuluh Nopember

Language: English

Topic: Graph Labeling and Dimension Problems

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Ministrstvo za visoko šolstvo, znanost in tehnologijo, Institut Teknologi Sepuluh Nopember, Lembaga Pengelola Dana Pendidikan

Awards: G3855682619, G8443298323