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A characterization for topologically integer additive set-indexer of graphs

    https://doi.org/10.1142/S1793830916500129Cited by:0 (Source: Crossref)

    The aim of this paper is to introduce a new function that satisfies the property of topological integer additive set-indexer (Top-IASI) with minimum cardinality for pan, tadpole, path and shovel graphs. Let GG be a graph and XX is a nonempty set. If an injective function f:V(G)P(X)f:V(G)P(X) induced a new injective function f:E(G)P(X){}f:E(G)P(X){} defined by f(uv)=f(u)f(v)f(uv)=f(u)f(v) for every uvE(G)uvE(G) then ff is called set-indexer. If an injective function f:V(G)P(N0)f:V(G)P(N0) produced another injective function f+:E(G)P(N0){}f+:E(G)P(N0){} defined by f+(uv)=f(u)+f(v)f+(uv)=f(u)+f(v) for every uvE(G)uvE(G), where N0N0 is the set of all non-negative integers and P(N0)P(N0) is its power set then ff is called an integer additive set-indexer (IASI). An IASI is called a Top-IASI if f(V(G)){}f(V(G)){} forms a topology.

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