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Let G1, G2, ..., Gn be a family of disjoint stars. The tree obtained by joining a new vertex a to one pendant vertex of each star Gi is called a banana tree. In this paper we determine the super edge-magic total labelings of the banana trees that have not been covered by the previous results [15].

We establish the existence of vertex-magic total labelings (VMTLs) for several infinite classes of regular graphs. The main method of construction is to assemble a number of appropriately labeled copies of one graph into a single graph with a VMTL. This method enables us for example to begin with any even-regular graph and from it construct a cubic graph possessing a VMTL. An important feature ...

Acharya and Hegde have introduced the notion of strongly k-indexable graphs: A (p, q)-graph G is said to be strongly k-indexable if its vertices can be assigned distinct integers 0, 1, 2, ..., p − 1 so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices can be arranged as an arithmetic progression k, k+ 1, k + 2, ..., k + (q − 1). Such an assignment ...

For a given graph G, let V be the number of vertices and E be the number of edges. Consider a labeling of the vertices and edges which is a one-to-one mapping of the set of integers {1, 2, . . . , V + E} onto the vertices and edges of the graph, with the property that for every vertex the sum of the labels assigned to that vertex and all edges incident with it is some constant k. Although work ...

Let G(V,E) be a graph and λ be a bijection from the set V ∪E to the set of the first |V |+ |E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say λ is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say λ is an (s, d) -vertex antimagic total (VAT) labeling if the vertex weights form an arithmetic pro...

The graphs considered in this paper are finite, undirected and simple. For a graph G, we denote its vertex set by V (G) and its edge set by E(G). A graph labeling, as introduced in [8], is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Over the years, a large variety of different types of graph labelings have been studied, see [2] for an extensive su...

In this paper, we consider a strongly repelling model of $n$ ordered particles $\{e^{i \theta_j}\}_{j=0}^{n-1}$ with the density $p({\theta_0},\dots, \theta_{n-1})=\frac{1}{Z_n} \exp \big\{-\frac{\beta}{2}\sum_{j \ne k} \sin^{-2} \big( \frac{\theta_j-\theta_k}{2}\big)\big\}$, $\beta>0$. Let $\theta_j=2 \pi j/n+x_j/n^2+{const}$ such that $\sum_{j=0}^{n-1}x_j=0$. Define $\zeta_n (2 j/n) =x_j/\sqr...