Switched signed graphs of integer additive set-valued signed graphs
Abstract
Let XX denote a set of non-negative integers and ๐ซ(X) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective set-valued function f:V(G)โ๐ซ(X)โ{โ } such that the induced function f+:E(G)โ๐ซ(X)โ{โ } is defined by f+(uv)=f(u)+f(v); โuvโE(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 ฯ defined by ฯ(uv)=(โ1)|f+(uv)|; โuvโE(S). A marking of a signed graph is an injective map ฮผ:V(S)โ{+,โ}, defined by ฮผ(v)=(โ1)|f(v)| for all vโV(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.
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