<p>Among the most studied graph labelings we have varieties called alpha and edge-magic. Even when their definitions seem completely different, these are related. A graceful labeling of a bipartite is an α-labeling if smaller labels assigned to vertices same stable set. An edge-magic size <em>n</em> said be <em>b</em>-edge consecutive its edges labeled with integer...

An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, ..., q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it admits an antimagic labeling. Hartsfield and Ringel conject...

A Γ -magic rectangle set MRSΓ (a, b; c) of order abc is a collection of c arrays (a× b) whose entries are elements of group Γ , each appearing once, with all row sums in every rectangle equal to a constant ω ∈ Γ and all column sums in every rectangle equal to a constant δ ∈ Γ . In the paper we show that if a and b are both even then MRSΓ (a, b; c) exists for any Abelian group Γ of order abc. Fu...

In this paper, we have proved edge-magic total labeling of cycles with P3 chords.

For any non negative real values h and k, an L(h, k)-labeling of a graph G = (V,E) is a function L : V → IR such that |L(u)− L(v)| ≥ h if (u, v) ∈ E and |L(u)− L(v)| ≥ k if there exists w ∈ V such that (u,w) ∈ E and (w, v) ∈ E. The span of an L(h, k)-labeling is the difference between the largest and the smallest value of L, so it is not restrictive to assume 0 as the smallest value of L. We de...

Let G be a graph of size n with vertex set V (G) and edge set E(G). A ρ-labeling of G is a one-to-one function h : V (G) → {0, 1, . . . , 2n} such that {min{|h(u)−h(v)|, 2n+1−|h(u)−h(v)|} : {u, v} ∈ E(G)} = {1, 2, . . . , n}. Such a labeling of G yields a cyclic G-decomposition of K2n+1. It is conjectured by El-Zanati and Vanden Eynden that every 2-regular graph G admits a ρ-labeling. We show t...

0079-6 doi:10. * Co Scienc Tokyo E-m 2.1. H labeling in early studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 2.2. Uniform N labeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 2.3. Amino acid type-selective Cand ...