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<p>A <i>b</i>-coloring of a graph <i>G</i> is a proper coloring of the vertices of <i>G</i> such that there exists a vertex in each color class joined to at least one vertex in each other color class. The <i>b</i>-chromatic number of a graph <i>G</i>, denoted by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varphi (\textit{G})\)</EquationSource> </InlineEquation>, is the largest integer <i>k</i> such that <i>G</i> has a <i>b</i>-coloring with <i>k</i> colors. In this paper, the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textit{b}\)</EquationSource> </InlineEquation>-chromatic number and <i>b</i>-chromatic sum of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((P_{n}\circ G)^{p}\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((P_{n}\circ G)^p\)</EquationSource> </InlineEquation> is the power graph of corona of the path <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(P_n\)</EquationSource> </InlineEquation> and <i>G</i> with power <i>p</i> is discussed. Also discussed the <i>b</i>-continuity property of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\((P_{n}\circ G)^{p}.\)</EquationSource> </InlineEquation></p>

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b-Coloring of Power Graph of Corona of Path and an Arbitrary Graph

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • P. C. Lisna,
  • M. S. Sunitha

摘要

A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least one vertex in each other color class. The b-chromatic number of a graph G, denoted by \(\varphi (\textit{G})\) , is the largest integer k such that G has a b-coloring with k colors. In this paper, the \(\textit{b}\) -chromatic number and b-chromatic sum of \((P_{n}\circ G)^{p}\) , where \((P_{n}\circ G)^p\) is the power graph of corona of the path \(P_n\) and G with power p is discussed. Also discussed the b-continuity property of \((P_{n}\circ G)^{p}.\)