Let G = (V (G), E(G)) be a finite simple graph with p = |V (G)| vertices and q = |E(G)| edges,without isolated vertices or isolated edges. A vertexmagic total labeling is a bijection from V (G) ∪ E(G) to the consecutive integers 1, 2, . . . , p + q, with the property that, for every vertex u in V (G), one has f (u) +  uv∈E(G) f (uv) = k for some constant k. Such a labeling is called E-super ve...

<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...

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

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.

We compute the equivariant cohomology $H^*_{T_I}(\mathcal Z_K)$ of moment-angle complexes $\mathcal Z_K$ with respect to action coordinate subtori $T_I \subset T^m$. give a criterion for formality and obtain specifications cases flag graphs.