Geodesic
Tosha-degree equivalence signed graphs
Vladikavkazskij matematičeskij žurnal, Tome 22 (2020) no. 2, pp. 48-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Tosha-degree 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 self-loops 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 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 $ k^{th}$ iterated Tosha-degree equivalence signed graphs. It is shown that for any signed graph $\Sigma$, its Tosha-degree equivalence signed graph $T(\Sigma)$ is balanced and we offer a structural characterization of Tosha-degree equivalence signed graphs. 
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     author = {R. Rajendra and P. Siva Kota Reddy},
     title = {Tosha-degree equivalence signed graphs},
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     pages = {48--52},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2020_22_2_a4/}
}
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R. Rajendra; P. Siva Kota Reddy. Tosha-degree equivalence signed graphs. Vladikavkazskij matematičeskij žurnal, Tome 22 (2020) no. 2, pp. 48-52. http://geodesic.mathdoc.fr/item/VMJ_2020_22_2_a4/

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