The theory of graphons is an important tool in understanding properties large networks. We investigate a power-law random graph model and cast it the graphon framework. distinctively different structures limit are explored detail sub-critical super-critical regimes. In regime, empty with high probability, rare event that non-empty, consists single edge. Contrarily, non-trivial exists limit, ser...

Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these is the emergence a power law. Power law behavior with different scaling factors can also be observed genealogical networks, but we still not satisfactorily describe its dynamics or relation to population evolution over time. In this paper, use an algorithm measure impa...

Many massive graphs (such as WWW graphs and Call graphs) share certain universal characteristics which can be described by socalled the “power law”. In this paper, we will first briefly survey the history and previous work on power law graphs. Then we will give four evolution models for generating power law graphs by adding one node/edge at a time. We will show that for any given edge density a...

The remarkable discovery of many large-scale real networks is the power-law distribution in degree sequence: the number of vertices with degree i is proportional to i−β for some constant β > 1. A lot of researchers believe that it may be easier to solve some optimization problems in powerlaw graphs. Unfortunately, many problems have been proved NP-hard even in power-law graphs. Intuitively, a t...

In this paper some coloring properties of graphs power have been presented. In this regard, the helical graphs have been introduced and it was shown that they are hom-universal with respect to high odd-girth graphs whose lth power is bounded with a Kneser graph. In the sequel, we have considered Pentagon’s problem of Nešetřil which this problem is about the existence of high girth cubic graphs ...

We present methods for drawing graphs that arise in various information networks. It has been noted that many realistic graphs have power law degree distribution and exhibit the small world phenomenon. Our algorithm is influenced by recent developments on modeling and analysis of such power law graphs.

The power graph of a group is the graph whose vertex set is the group, two elements being adjacent if one is a power of the other. We observe that nonisomorphic finite groups may have isomorphic power graphs, but that finite abelian groups with isomorphic power graphs must be isomorphic. We conjecture that two finite groups with isomorphic power graphs have the same number of elements of each o...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.