The directed power graph G?(G) of a group G is the simple digraph with vertex set such that x?y if y x. G, denoted by G(G), underlying graph. In this paper, for groups and H, following proved. If has no quasicyclic subgroup Cp? which trivial intersection every cyclic K K??Cp?, then G(G)?G(H) implies G?(G)?G?(H). particular, any two torsion-free having isomorphic graphs have graphs.

Knowledge graphs are a key technique for linking and integrating cross-domain data, concepts, tools, knowledge to enable data-driven analytics. As much of the world's data have become massive in size, visualizing graph entities their interrelationships intuitively interactively has crucial task ingesting better utilizing content support semantic reasoning, discovering hidden discovering, scient...

We introduce and explore random conformal graph directed Markov systems governed by measure-preserving ergodic dynamical systems. We first develop the symbolic thermodynamic formalism for random finitely primitive subshifts of finite type with a countable alphabet (by establishing tightness in a narrow topology). We then construct fibrewise conformal and invariant measures along with fibrewise ...

This paper addresses the problem of aggregating the topology of a sub-network in a compact way with minimum distortion. The problem arises from networks that have a hierarchical structure , where each sub-network must advertise the cost of routing between each pair of its border nodes. The straightforward solution of advertising the exact cost for each pair has a quadratic cost which is not pra...

This note generalizes the (a, b)-coloring game and the (a, b)-marking game which were introduced by Kierstead [7] for undirected graphs to directed graphs. We prove that the (a, b)-chromatic and (a, b)-coloring number for the class of orientations of forests is b + 2 if b ≤ a, and infinity otherwise. From these results we deduce upper bounds for the (a, b)-coloring number of oriented outerplana...

We address how the structure of a social communication system affects language coordination. The naming game is an abstraction of lexical acquisition dynamics, in which N agents try to find an agreement on the names to give to objects. Most results on naming games are specific to certain communication network topologies. We present two important results that are general to any graph topology: t...

In this paper, a novel image registration method is proposed to achieve accurate registration between images having large shape differences with the help of a set of appropriate intermediate templates. We first demonstrate that directionality is a key factor in both pairwise image registration and groupwise registration, which is defined in this paper to describe the influence of the registrati...