Switching Invariant Neighborhood Signed Graphs
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A signed graph (marked graph) is an ordered pair S = (G, ) (S = (G, μ)),where G = (V,E) is a graph called the underlying graph of S and [수식] is a function. The neighborhood graph of a graph G = (V,E), denoted by N(G),is a graph on the same vertex set V , where two vertices in N(G) are adjacent if, and only if, they have a common neighbor. Analogously, one can define the neighborhood signed graph N(S) of a signed graph [수식] as a signed graph,[수식] where N(G) is the underlying graph of N(S), and for any edge e = uv in N(S),[수식] where for any v 2 V , μ(v) =Y u)μ(v), where for any v 2 V , μ(v) = u2N(v) (uv). In this paper, we characterize signed graphs S for which S N(S), Sc N(S) and N(S) J(S), where J(S) and Sc denotes jump signed graph and complement of signed graph of S respectively.
Abstract
A signed graph (marked graph) is an ordered pair S = (G, ) (S = (G, μ)),where G = (V,E) is a graph called the underlying graph of S and [수식] is a function. The neighborhood graph of a graph G = (V,E), denoted by N(G),is a graph on the same vertex set V , where two vertices in N(G) are adjacent if, and only if, they have a common neighbor. Analogously, one can define the neighborhood signed graph N(S) of a signed graph [수식] as a signed graph,[수식] where N(G) is the underlying graph of N(S), and for any edge e = uv in N(S),[수식] where for any v 2 V , μ(v) =Y u)μ(v), where for any v 2 V , μ(v) = u2N(v) (uv). In this paper, we characterize signed graphs S for which S N(S), Sc N(S) and N(S) J(S), where J(S) and Sc denotes jump signed graph and complement of signed graph of S respectively.
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