Let $A$ be an abelian group. A graph $G=(V,E)$ is said to be $A$-barycentric-magic if there exists a labeling $l:E(G)longrightarrow Asetminuslbrace{0}rbrace$ such that the induced vertex set labeling $l^{+}:V(G)longrightarrow A$ defined by $l^{+}(v)=sum_{uvin E(G)}l(uv)$ is a constant map and also satisfies that $l^{+}(v)=deg(v)l(u_{v}v)$ for all $v in V$, and for some vertex $u_{v}$ adjacent t...

We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. We establish that the odd 8-vertex model is equivalent to a staggered 8-vertex model. Using this equivalence we deduce the solution of the odd 8-vertex ...

Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the difference between maximum and minimum of the distances of the vertex to the vertices of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced sub...

In this work some new odd graceful graphs are investigated. We prove that the graph obtained by fusing all the n vertices of Cn of even order with the apex vertices of n copies of K1,m admits odd graceful labeling. In addition to this we show that the shadow graphs of path Pn and star K1,n are odd graceful graphs.

A radio mean labeling of a connected graph G is a one to one map f from the vertex set V (G) to the set of natural numbers N such that for each distinct vertices u and v of G, d (u, v)+ ⌈ f(u)+f(v) 2 ⌉ ≥ 1+ diam (G). The radio mean number of f , rmn (f), is the maximum number assigned to any vertex of G.The radio mean number of G, rmn (G) is the minimum value of rmn (f) taken over all radio mea...

A graph labeling is an assignment of integers to the vertices (or) edges or both subject to certain conditions. Graceful labeling was introduced by Rosa [6] while the concept of odd graceful labeling was introduced by Gnanajothi [2]. A Graph G (V, E), |V(G)| = p, |E(G)| = q is said to be odd graceful if there is an injection from V(G) to {0, 1, 2, .... 2q-1} such that when each edge xy is assig...

A Radio Heronian Mean Dd-distance Labeling of a connected graph is an injective map from the vertex set N such that for two distinct vertices and , Dd where denotes between Dd-diameter G.