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DOI: 10.46698/m411373505686a ToshaDegree Equivalence Signed Graphs
Abstract:
The Toshadegree of an edge \(\alpha \) in a graph \(\Gamma\) without multiple edges, denoted by \(T(\alpha)\), is the number of edges adjacent to \(\alpha\) in \(\Gamma\), with selfloops counted twice. A signed graph (marked graph) is an ordered pair \(\Sigma=(\Gamma,\sigma)\) (\(\Sigma =(\Gamma, \mu)\)), where \(\Gamma=(V,E)\) is a graph called the underlying graph of \(\Sigma\) and \(\sigma : E \rightarrow \{+,\}\) (\(\mu : V \rightarrow \{+,\}\)) is a function. In this paper, we define the Toshadegree equivalence signed graph of a given signed graph and offer a switching equivalence characterization of signed graphs that are switching equivalent to Toshadegree equivalence signed graphs and \( k^{th}\) iterated Toshadegree equivalence signed graphs. It is shown that for any signed graph \(\Sigma\), its Toshadegree equivalence signed graph \(T(\Sigma)\) is balanced and we offer a structural characterization of Toshadegree equivalence signed graphs.
Keywords: signed graphs, balance, switching, Toshadegree of an edge, Toshadegree equivalence signed graph, negation.
Language: English
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For citation: Rajendra, R. and Reddy, P. S. K. ToshaDegree Equivalence Signed Graphs,
Vladikavkaz Math. J., 2020, vol. 22, no. 2, pp. 4852.
DOI 10.46698/m411373505686a← Contents of issue 
 

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