Scholarlink

<p>Let <i>k</i> be a positive integer. A <i>k</i>-tuple total dominator coloring of a graph <i>G</i> (abbreviated as <i>k</i>TD-coloring) is a proper coloring of <i>G</i> such that each vertex of the graph is adjacent to every vertex of <i>k</i> color classes. The <i>k</i>-tuple total dominator chromatic number, denoted by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\chi _{k,d}^t\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>χ</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> </math></EquationSource> </InlineEquation>, is the minimum number of colors among all <i>k</i>TD-colorings. In this paper, we present an extensive study of <i>k</i>TD-coloring of graphs. First, we describe some useful bounds involving <i>k</i>-tuple total dominator chromatic number. We also find bounds for the <i>k</i>-tuple total dominator chromatic number of the corona product and the edge corona product of the graphs. Finally, we examine the effects on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\chi _{k,d}^t\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>χ</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> </math></EquationSource> </InlineEquation> when <i>G</i> is modified by some operations. The effect of modifying the graph on the parameter is of practical importance.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An extensive study on the k-tuple total dominator chromatic number of graphs

  • 期刊论文

  • 发表日期：

    2025年10月15日

查看全文
  • Fairouz Beggas,
  • Walid Marweni

摘要

Let k be a positive integer. A k-tuple total dominator coloring of a graph G (abbreviated as kTD-coloring) is a proper coloring of G such that each vertex of the graph is adjacent to every vertex of k color classes. The k-tuple total dominator chromatic number, denoted by \(\chi _{k,d}^t\) χ k , d t , is the minimum number of colors among all kTD-colorings. In this paper, we present an extensive study of kTD-coloring of graphs. First, we describe some useful bounds involving k-tuple total dominator chromatic number. We also find bounds for the k-tuple total dominator chromatic number of the corona product and the edge corona product of the graphs. Finally, we examine the effects on \(\chi _{k,d}^t\) χ k , d t when G is modified by some operations. The effect of modifying the graph on the parameter is of practical importance.