Dominated Coloring of Certain Graphs
Publish place: Global Analysis And Discrete Mathematics، Vol: 7، Issue: 1
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_GADM-7-1_008
تاریخ نمایه سازی: 8 آذر 1401
Abstract:
A proper coloring of a graph G is called a dominated coloring whenever each color class is dominated by at least one vertex. The minimum number of colors among all dominated colorings of G is called its dominated chromatic number, denoted by χdom(G). We define a parameter related to dominated coloring, namely dominated chromatic covering. For a minimum dominated coloring of G, a set of vertices S is called a dominated chromatic covering if each color class is dominated by a vertex of S. The minimum cardinality of a dominated chromatic covering of G is called its dominated chromatic covering number, denoted by θχdom(G) . It is clear that θχdom(G) ≤ χdom(G). In this paper, we obtain the dominated chromatic number and θχdom(G) when G is middle and total graph of paths and cycles.
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Authors
Fatemeh Choopani
Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Abbas Jafarzadeh
Department of Mathematics, Quchan University of Technology, Quchan, Iran
Doost Ali Mojdeh
Department of Mathematics, University of Mazandaran, Babolsar, Iran
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