Tosha-degree equivalence signed graphs
Автор: Rajendra Rangaswamy, Reddy Polaepalli Siva Kota
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 2 т.22, 2020 года.
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The Tosha-degree of an edge α in a graph Γ without multiple edges, denoted by T(α), is the number of edges adjacent to α in Γ, with self-loops counted twice. A signed graph (marked graph) is an ordered pair Σ=(Γ,σ) (Σ=(Γ,μ)), where Γ=(V,E) is a graph called the underlying graph of Σ and σ:E→{+,-} (μ:V→{+,-}) is a function. In this paper, we define the Tosha-degree equivalence signed graph of a given signed graph and offer a switching equivalence characterization of signed graphs that are switching equivalent to Tosha-degree equivalence signed graphs and kth iterated Tosha-degree equivalence signed graphs. It is shown that for any signed graph Σ, its Tosha-degree equivalence signed graph T(Σ) is balanced and we offer a structural characterization of Tosha-degree equivalence signed graphs.
Signed graphs, balance, switching, tosha-degree of an edge, tosha-degree equivalence signed graph, negation
Короткий адрес: https://sciup.org/143170644
IDR: 143170644 | DOI: 10.46698/m4113-7350-5686-a
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