SOME NEW RESULTS ON INTEGER ADDITIVE SET-VALUED SIGNED GRAPHS

Abstract : Let X denotes a set of non-negative integers and P(X) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective set-valued function f : V (G) → P(X) − {∅} such that the induced function f+ : E(G) → P(X) − {∅} is defined by f+(uv) = f(u) + f(v); ∀ uv ∈ E(G), where f(u) + f(v) is the sumset of f(u) and f(v). An IASL of a signed graph is an IASL of its underlying graph G together with the signature σ defined by σ(uv) = (−1)|f+(uv)| ; ∀ uv ∈ E(Σ). In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive set-labelings.
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Sudev Naduvath, P Ashraf, K. Germina. SOME NEW RESULTS ON INTEGER ADDITIVE SET-VALUED SIGNED GRAPHS. TWMS Journal of Applied and Engineering Mathematics, Turkish World mathematical Society, 2019, 9 (3), pp.638-645. ⟨http://jaem.isikun.edu.tr/web/index.php/archive/102-vol9no3/447-some-new-results-on-integer-additive-set-valued-signed-graphs⟩. ⟨hal-02263299⟩

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