SEMT Labelings and Deficiencies of Forests with Two Components (II)

Abstract

Given a simple graph G(V, E), consider a bijective function Γ from V (G) ∪ E(G) to [ν + ε], where ν = |V (G)| = order of G, ε = |E(G)| = size of G. If for all e = xy ∈ E(G), Γ(x) + Γ(e) + Γ(y) is a constant, then Γ is called an edge-magic total (EMT) labeling. Moreover, if Γ(V (G)) = [ν], then Γ is a super edge-magic total (SEMT) labeling of G and G is a SEMT graph. If a graph G has at least one SEMT labeling then the smallest of the magic constants for all possible distinct SEMT labelings of G describes super edge-magic total (SEMT) strength, sm(G), of G. For any graph G, SEMT deficiency is the least number of isolated vertices which when uniting with G yields a SEMT graph. This paper focuses on finding SEMT strength of generalized comb Cbτ (2, 3, . . . , τ +1) and evaluating SEMT labeling and deficiency of forests be composed of two components, where one of the components for each forest is aforesaid generalized comb and other component is star, bistar, comb, path respectively.