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- W3094301876 abstract "A subset <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi>S</mi> </math> of <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi>V</mi> <mfenced open=( close=) separators=|> <mrow> <mi>G</mi> </mrow> </mfenced> </math> is called a total dominating set of a graph <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <mi>G</mi> </math> if every vertex in <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <mi>V</mi> <mfenced open=( close=) separators=|> <mrow> <mi>G</mi> </mrow> </mfenced> </math> is adjacent to a vertex in <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi>S</mi> </math> . The total domination number of a graph <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <mi>G</mi> </math> denoted by <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mfenced open=( close=) separators=|> <mrow> <mi>G</mi> </mrow> </mfenced> </math> is the minimum cardinality of a total dominating set in <math xmlns=http://www.w3.org/1998/Math/MathML id=M8> <mi>G</mi> </math> . The maximum order of a partition of <math xmlns=http://www.w3.org/1998/Math/MathML id=M9> <mi>V</mi> <mfenced open=( close=) separators=|> <mrow> <mi>G</mi> </mrow> </mfenced> </math> into total dominating sets of <math xmlns=http://www.w3.org/1998/Math/MathML id=M10> <mi>G</mi> </math> is called the total domatic number of <math xmlns=http://www.w3.org/1998/Math/MathML id=M11> <mi>G</mi> </math> and is denoted by <math xmlns=http://www.w3.org/1998/Math/MathML id=M12> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mfenced open=( close=) separators=|> <mrow> <mi>G</mi> </mrow> </mfenced> </math> . Domination in graphs has applications to several fields. Domination arises in facility location problems, where the number of facilities (e.g., hospitals and fire stations) is fixed, and one attempts to minimize the distance that a person needs to travel to get to the closest facility. In this paper, the numerical invariants concerning the total domination are studied for generalized Petersen graphs." @default.
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- W3094301876 date "2020-10-24" @default.
- W3094301876 modified "2023-10-17" @default.
- W3094301876 title "The Numerical Invariants concerning the Total Domination for Generalized Petersen Graphs" @default.
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- W3094301876 doi "https://doi.org/10.1155/2020/5473675" @default.
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