Graph products are characterized by the existence of non-trivial equivalence relations on the edge set of a graph that satisfy a so-called square property. We investigate here a generalization, termed RSP-relations. The class of graphs with non-trivial RSP-relations in particular includes graph bundles. Furthermore, RSP-relations are intimately related with covering graph constructions. For K2,...

The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.

The boxicity (cubicity) of a graph G is the minimum natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes (axis-parallel unit cubes) in Rk. In this article, we give estimates on the boxicity and the cubicity of Cartesian, strong and direct products of graphs in terms of invariants of the component graphs. In particular, we study the growth, ...

This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local approach that covers a graph by small subgraphs, so-called partial star products, and then utilizes this information to derive the global factors and an embeddin...

Sparse matrix-matrix products appear in multigrid solvers and computational methods for graph theory. Some formulations of these products require the inner product of two sparse vectors, which have inefficient use of cache memory. In this paper, we propose a new algorithm for computing sparse matrix-matrix products by exploiting matrix nonzero structure through the process of graph coloring. We...

the edge szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph g, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. in this paper, the edge szeged index of one-pentagonal carbon nanocone cnc5[n] is computed for the first ...

The edge Szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph G, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. In this paper, the edge Szeged index of one-pentagonal carbon nanocone CNC5[n] is computed for the first ...

This study is concerned with how the quality of perishable products can be improved by shortening the time interval between production and distribution. As special types of food such as dairy products decay fast, the integration of production and distribution scheduling (IPDS) is investigated. An integrated scheduling of both processes improves the performance and costs because the separated sc...