Coloring of Non-Zero Component Graphs

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-5962

Keywords:

Non-zero component graph, graph coloring, chromatic number.

Abstract

The non-zero component graph of finite dimensional vector space over a finite field $F$ is the graph $G = (V,E)$, where vertices of $G$ are the non-zero vectors in $V$, two of which are adjacent if they share at least one basis vector with non-zero coefficient in their basic representation. In this paper, we study the various types of colorings of non-zero component graph.

References

L. W. Beineke, R. J. Wilson, and P. J. Cameron. Topics in algebraic graph theory, volume 102. Cambridge University Press, 2004.

G. Chartrand, T. W. Haynes, M. A. Henning, and P. Zhang. From domination to coloring: Stephen Hedetniemi's graph theory and beyond. Springer Nature, 2019.

A. Das. Non-zero component graph of a finite-dimensional vector space. Comm. Algebra, 44(9):3918{3926, 2016.

A. Das. Non-zero component union graph of a finite-dimensional vector space. Linear Multilinear Algebra, 65(6):1276{1287, 2017.

A. Das. On non-zero component graph of vector spaces over finite fields. J. Algebra Appl., 16(01):1750007:1{10, 2017.

A. Das. On subspace inclusion graph of a vector space. Linear Multilinear Algebra, 66(3):554{564, 2018.

C. D. Godsil and M. W. Newman. The automorphism group and fixing number of orthogonality graph over a vector space. SIAM J. Discrete Math., 22(2): 683-692, 2008.

J. Kok, S. Naduvath, and M. K. Jamil. Rainbow neighbourhood number of graphs. Proyecciones(Antofagasta), 38(3):469{484, 2019.

V. M. Mathew and S. Naduvath. On non-zero component graphs of finite dimensional vector spaces. Lecture Notes Netw. Syst., 2021.

V. M. Mathew, S. Naduvath, and I. N. Cangul. Some vertex degree-based topological indices of non-zero component graphs. Communicated, 2022.

V. M. Mathew, S. Naduvath, and T. V. Joseph. On orthogonal component graphs of vector spaces over the eld Zp. Proyecciones J. Math, To appear, 2023.

S. Naduvath and J. Kok. J- coloring of graph operations. Acta Univ. Sapientia, Inform., 11(1):95{108, 2019.

S. Ou and Y. Tan. The automorphism group and fixing number of orthogonality graph over a vector space. J. Algebra Appl., 20(12), 2021.

D. B. West. Introduction to graph theory. Prentice Hall of India, New Delhi, 2001.

Published

2024-06-19

How to Cite

[1]
V. Mary Mathew and S. Naduvath, “Coloring of Non-Zero Component Graphs”, Proyecciones (Antofagasta, On line), vol. 43, no. 4, pp. 883-898, Jun. 2024.

Issue

Section

Artículos