Graph products have important role in constructing many useful networks. It is known that there are four basic graph products. Properties of each product have been studied individually. We propose a unified approach to these products based on the distance in graphs, and new two products on graphs. The viewpoint of products based on the distance introduced here provides a family of products that...

Graph burning is a deterministic discrete time graph process that can be interpreted as a model for the spread of influence in social networks. The burning number of a graph is the minimum number of steps in a graph burning process for that graph. In this paper, we consider the burning number of graph products. We find some general bounds on the burning number of the Cartesian product and the s...

Radio labeling is derived from the assignment of radio frequencies (channels) to a set of transmitters. The frequencies assigned depend on the geographical distance between the transmitters: the closer two transmitters are, the greater the potential for interference between their signals. Thus when the distance between two transmitters is small, the difference in the frequencies assigned must b...

For certain graphs, we can associate a universal C*-algebra, which encodes the information of the graph algebraically. In this paper we examine the relationships between products of graphs and their associated C*-algebras. We present the underlying theory of associating a C*-algebra to a direct graph as well as to a higher rank graph. We then provide several isomorphisms relating C*-algebras of...