Resolvable even cycle decompositions of the tensor product of complete graphs

Tutte Polynomials of Flower Graphs

Resolvable gregarious cycle decompositions of complete equipartite graphs

The complete multipartite graph Kn(m) with n parts of size m is shown to have a decomposition into n-cycles in such a way that each cycle meets each part of Kn(m); that is, each cycle is said to be gregarious. Furthermore, gregarious decompositions are given which are also resolvable. © 2007 Elsevier B.V. All rights reserved.

Wiener Polarity Index of Tensor Product of Graphs

Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index ...

Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

On Tensor Product of Graphs, Girth and Triangles

The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.