ON THE PALETTE INDEX OF GRAPHS HAVING A SPANNING STAR

Authors

  • Aghasi B. Ghazaryan Chair of Discrete Mathematics and Theoretical Informatics, YSU, Armenia
  • Petros A. Petrosyan Chair of Discrete Mathematics and Theoretical Informatics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2022.56.3.085

Keywords:

edge coloring, palette index, spanning star, complete split graph, threshold graph

Abstract

A proper edge coloring of a graph $G$ is a mapping $\alpha:E(G)\longrightarrow \mathbb{N}$ such that $\alpha(e)\not=\alpha(e')$ for every pair of adjacent edges $e$ and $e'$ in $G$. In a proper edge coloring of a graph $G$, the palette of a vertex $v \in V(G)$ is the set of colors assigned to the edges incident to $v$. The palette index of $G$ is the minimum number of distinct palettes occurring in $G$ among all proper edge colorings of $G$. A graph $G$ has a spanning star, if it has a spanning subgraph which is a star. In this paper, we consider the palette index of graphs having a spanning star. In particular, we give sharp upper and lower bounds on the palette index of these graphs. We also provide some upper and lower bounds on the palette index of the complete split and threshold graphs.

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Published

2022-10-17

How to Cite

Ghazaryan, A. B., & Petrosyan, P. A. (2022). ON THE PALETTE INDEX OF GRAPHS HAVING A SPANNING STAR. Proceedings of the YSU A: Physical and Mathematical Sciences, 56(3 (259), 85–96. https://doi.org/10.46991/PYSU:A/2022.56.3.085

Issue

Section

Mathematics