SOME NEW RESULTS ON INTEGER ADDITIVE SET-VALUED SIGNED GRAPHS

Sudev Naduvath (1) , P K Ashraf (2) , K. A Germina (3)

1 Christ University, Bangalore
2 Government Arts & Science College
3 CUK - Central University of Kerala

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.

Mots clés: integer additive set-labeled signed graphs; arithmetic integer additive set-labeled signed graphs; clustering of signed graphs; balanced signed graphs; Signed graphs

Domaines: Combinatoire [math.CO]

Sudev Naduvath, P K Ashraf, K. A Germina. SOME NEW RESULTS ON INTEGER ADDITIVE SET-VALUED SIGNED GRAPHS. TWMS Journal of Applied and Engineering Mathematics, 2019, 9 (3), pp.638-645. ⟨hal-02263299⟩