We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models. Moreover, clustering coefficient of these graphs can also be controlled. We propose a concrete flexible model from our class and provide an efficient algorith...

Vertex pursuit games, such as the game of Cops and Robber, are a simplified model for network security. In these games, cops try to capture a robber loose on the vertices of the network. The minimum number of cops required to win on a graph G is the cop number of G. We present asymptotic results for the game of Cops and Robber played in various stochastic network models, such as in G(n, p) with...

Vertex pursuit games, such as the game of Cops and Robbers, are a simplified model for network security. In these games, cops try to capture a robber loose on the vertices of the network. The minimum number of cops required to win on a graph G is the cop number of G. We present asymptotic results for the game of Cops and Robbers played in various stochastic network models, such as in G(n, p) wi...

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Zn and edge set {{a, b} : a, b ∈ Zn, gcd(a− b, n) ∈ D}. Using tools from convex optimization, we study the maxim...