Star coloring splitting graphs of cycles

TL;DR

This paper determines the star chromatic number of splitting graphs of cycles for specific lengths, resolving an open question in graph coloring theory.

Contribution

It provides the exact star chromatic number for splitting graphs of cycles of certain lengths, advancing understanding of star colorings in graph theory.

Findings

Star chromatic number for splitting graphs of cycles with n ≡ 1 mod 3

Star chromatic number for splitting graph of cycle of length 5

Resolved an open question in the literature

Abstract

A star coloring of a graph $G$ is a proper vertex coloring such that the subgraph induced by any pair of color classes is a star forest. The star chromatic number of $G$ is the minimum number of colors needed to star color $G$. In this paper we determine the star-chromatic number of the splitting graphs of cycles of length $n$ with $n \equiv 1 \pmod 3$ and $n=5$, resolving an open question of Furnma\'nczyk, Kowsalya, and Vernold Vivin.