‎‎for any group $g$‎, ‎we define an equivalence relation $thicksim$ as below‎: ‎[forall g‎, ‎h in g gthicksim h longleftrightarrow |g|=|h|]‎ ‎the set of sizes of equivalence classes with respect to this relation is called the same-order type of $g$ and denote by $alpha{(g)}$‎. ‎in this paper‎, ‎we give a partial answer to a conjecture raised by shen‎. ‎in fact‎, ‎we show that if $g$ is a nilpot...

Graphical Markov models determined by acyclic digraphs (ADGs), also called directed acyclic graphs (DAOs), are widely studied in statistics, computer science (as Bayesian networks), operations research (as influence diagrams), and many related fields. Because different ADOs may determine the same Markov equivalence class, it long has been of interest to determine the efficiency gained in model ...

The independence equivalence class of a graph $G$ is the set graphs that have same polynomial as $G$. Beaton, Brown and Cameron (arXiv:1810.05317) found classes even cycles, raised problem finding odd cycles. completely solved in this paper.

In this work, we represent complex video activities as one large activity graph and propose a constraint based graph mining technique to discover a partonomy of classes of subgraphs corresponding to event classes. Events are defined as subgraphs of the activity graph that represent what we regard as interesting interactions, that is, where all objects are actively engaged and are characterized ...

The local complementation rule is applied for continuous-variable (CV) graph states in the paper, which is an elementary graph transformation rule and successive application of which generates the orbit of any graph states. The corresponding local Gaussian transformations of local complementation for four-mode unweighted graph states were found, which do not mirror the form of the local Cliffor...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

The Shannon capacity of every induced subgraph of a perfect graph equals its clique number. However, for the co{normal powers of an odd cycle the super{multiplicativity of the clique number makes the determination of capacity one of the hardest problems in combinatorics. We study the asymptotic growth of induced subgraphs of some particular type in powers of a xed graph. In case of a simple gra...