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Switched signed graphs of integer additive set-valued signed graphs

    https://doi.org/10.1142/S1793830917500434Cited by:2 (Source: Crossref)

    Let XX denote a set of non-negative integers and ๐’ซ(X) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective set-valued function f:V(G)โ†’๐’ซ(X)โˆ’{โˆ…} such that the induced function f+:E(G)โ†’๐’ซ(X)โˆ’{โˆ…} is defined by f+(uv)=f(u)+f(v); โˆ€uvโˆˆE(G), where f(u)+f(v) is the sumset of f(u) and f(v). An IASL of a signed graph S is an IASL of its underlying graph G together with the signature ฯƒ defined by ฯƒ(uv)=(โˆ’1)|f+(uv)|; โˆ€uvโˆˆE(S). A marking of a signed graph is an injective map ฮผ:V(S)โ†’{+,โˆ’}, defined by ฮผ(v)=(โˆ’1)|f(v)| for all vโˆˆV(S). Switching of signed graph is the process of changing the sign of the edges in S whose end vertices have different signs. In this paper, we discuss certain characteristics of the switched signed graphs of certain types of integer additive set-labeled signed graphs.

    AMSC: 05C78, 05C22
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