Let G be a group. The power graph of G is a graph with the vertex set G, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique/chromatic number. Furthermore, it is proved that for every grou...

in this paper by using concepts of graph theory, forces method and substructure ing method for analysis of structures, some methods have been introduced for optimal analysis of structures in a large scale, using substructuring method. planar rigid frames assuming linear behavior and small deformations, have been optimal analyzed, by using forces method. thus, a fortran power station computation...

Structural codes vis-a-vis structural counts, like polynomials of a molecular graph, are important in computing graph-theoretical descriptors which are commonly known as topological indices. These indices are most important for characterizing carbon nanotubes (CNTs). In this paper we have computed Sadhana index (Sd) for phenylenes and their hexagonal squeezes using structural codes (counts). Sa...

A graph generator is a tool which allows to create graph-like data whose structural properties are very similar those found in real world networks. This paper presents two methods generate graphs with power-law edge distribution based on the MapReduce processing model that can be easily implemented run top of Apache Hadoop. The proposed allow generation directed and undirected distributed witho...

The power graph P(G) of a group G is with vertex set G, where two vertices u and v are adjacent if only u≠v um=v or vm=u for some positive integer m. In this paper, we raise study the following question: For which natural numbers n every groups order isomorphic graphs isomorphic? particular, it proved that all such odd number cube-free also they not multiples 16 in general. Moreover, show finit...