Manuscript Title:

VARIATION OF EQUITABLE COLOR CLASS DOMINATION NUMBER AFTER THE LINK REMOVAL IN GRAPHS

Author:

A. ESAKKIMUTHU, S. MARI SELVAM, VASANTHI S, GNANAVIJI D

DOI Number:

DOI:10.5281/zenodo.8289140

Published : 2023-08-23

About the author(s)

1. A. ESAKKIMUTHU - Assistant Professor, PG and Research, Department of Mathematics, Kamaraj College, Thoothukudi, Tamilnadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, Tamilnadu, India.
2. S. MARI SELVAM - Research Scholar, Reg. No: 21212102091009, PG and Research, Department of Mathematics, Kamaraj College, Thoothukudi, Tamilnadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, Tamilnadu, India.
3. VASANTHI S - Assistant Professor, Mathematics, CSI Jayaraj Annapackiam College, Nallur, Tamilnadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, Tamilnadu, India.
4. GNANAVIJI D - Assistant Professor, Mathematics, CSI Jayaraj Annapackiam College, Nallur, Tamilnadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, Tamilnadu, India.

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Abstract

Let 𝐺 = (𝑉, 𝐸) be a connected graph. Assume a group 𝐢𝐢 containing colors. Let 𝜏 ∢ 𝑉(𝐺) → 𝐢𝐢 be an equitably colorable function. A dominating subset 𝑆 of 𝑉 is called an equitable color class dominating set if the number of dominating nodes in each color class is equal. The least possible cardinality of an equitable color class dominating set of 𝐺 is called the equitable color class domination number itself. It is indicated by 𝛾𝐸𝐢𝐢(𝐺). In this paper, we study the changing and unchanging of 𝐸𝐢𝐢 Domination number after the link removal.


Keywords

Dominating Set, Equitable Coloring, Color Class (𝐢𝐢), Equitable Color Class (𝐸𝐢𝐢), Equitable Color Class Dominating Set, Link Removal.