For any non-trivial abelian group A under addition a graph G is said to be A-Magic if there exists a labeling f: E(G) → A − {0} such that, the vertex labeling f+ defined as f+(v) = P f(uv) taken over all edges uv incident at v is a constant. An A-Magic graph G is said to be Zk-Magic graph if the group A is Zk the group of integers modulo k. These Zk-Magic graphs are referred to as k-Magic graphs. In this paper we prove that the total graph, flower graph, generalized prism graph, closed helm graph, lotus inside a circle graph, G ⊙ Km, m-splitting graph of a path and m-shadow graph of a path are Zk-Magic graphs.

A (p, q)-graph G is (a, d)-edge antiMagic total if there exists a bijection f from V (G) ∪ E(G) to {1, 2, . . ., p + q} such that for each edge uv ∈ E(G), the edge weight Λ(uv) = f(u) + f(uv) + f(v) forms an arithmetic progression with first term a > 0 and common difference d ≥ 0. An (a, d)-edge antiMagic total labeling in which the vertex labels are 1, 2, . . ., p and edge labels are p + 1, p + 2, . . ., p + q is called a super (a, d)-edge antiMagic total labeling. Another variant of (a, d)-edge antiMagic total labeling called as e-super (a, d)-edge antiMagic total labeling in which the edge labels are 1, 2, . . ., q and vertex labels are q + 1, q + 2, . . ., q + p. In this paper, we investigate the existence of e-super (a, d)-edge antiMagic total labeling for total graphs of paths, copies of cycles and disjoint union of cycles.

Suppose each edge of a simple connected undirected graph is given a unique number from the numbers $1, 2, \dots, $q$, where $q$ is the number of edges of that graph. Then each vertex is labelled with sum of the labels of the edges incident to it. If no two vertices have the same label, then the graph is called an antiMagic graph. We prove that the Cartesian product of wheel graph and path graph is antiMagic.

A type (1,1,1) face-Magic labeling of a planar graph G = (V, E,F) is a bijection from V ,E ,F to the set of labels {1,2, …, , |V|+ |E| + |F|} such that the weight of every n-sided face of G is equal to the same _xed constant. The weight of a face Ƒ,,F is equal to the sum of the labels of the vertices, edges, and face that determine Ƒ, . It is known that the grid graph Pm_Pn admits a type (1,1,1) face-Magic labeling, but the proof in the literature is quite lengthy. We give a simple proof of this result and show two more in_nite families of gridded graphs admit type (1,1,1) face-Magic labelings.

The mystical texts while including some secrets, mystery, conceptual and meaning complications and also using the symbolic, impressive, Magic and tuneful language, differ from the others literary and non-literary texts considerably. These differences are only considered by some of the intellectuals as the differences in language structure and know the meaning related complexity originated in the especial features of that language. Opposed to the mentioned viewpoints, this essay brings the priority of the concept and meaning over the language in mystical texts into sharp focus and reveals that revelation, understanding, interpretation and explanation of the meaning have priority over the terms and appropriateness of the language. Although the new findings based on revelation of meaning and concept creates a new language, it will be different from the other languages. In this regard, the understanding and interpretation by the general interpreters upon a the Holy Quran verses as well as the Khorasan mystics and Ibne Arabi"s ones in Fososelhekam, have been studied. The result of this essay and study have shown that meaning has priority over the terms and thought, in mystical texts. It also shows that the complementary development of the mystics" understanding of the Holy Quran till the period of Ibne Arabi and their effects and interplay on each other.

Let A be an abelian group. A graph G = (V, E) is said to be A-barycentric-Magic if there exists a labeling l: E (G) ®A\{0} such that the induced vertex set labeling l+ : V (G) ®A defined by l+ (v) =  å uvÎE(G) l (uv) is a constant map and also satisfies that l+ (v) = deg (v) l (uvv) for all v Î V, and for some vertex uv adjacent to v. In this paper we determine all h Î N for which a given graph G is Zh-barycentricMagic and characterize Zh-barycentric-Magic labeling for some graphs containing vertices of degree 2 and 3.

The article deals with a study of the phenomenon of Magic in certain ancient human rites. This is followed up by some manifestations of Magic, together with some instances of it as used in Persian literary texts. Important is that a study of Magic and its manifestations and the literary devices employed when talking about it are necessary to solve some problems inherent in some texts of Persian prose and poetry.