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.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

The present work proposes a possible solution to extend graphical models for correlated data. Particularly, the paper focused on hierarchical data structures, considering two-level random intercept models. The proposed solution allows to use the existing chain graphs theory in a straightforward way. After a brief introduction to multilevel models and a description of the conditional independenc...

In this paper we study the expressiveness of the AnderssonMadigan-Perlman interpretation of chain graphs. It is well known that all independence models that can be represented by Bayesian networks also can be perfectly represented by chain graphs of the Andersson-MadiganPerlman interpretation but it has so far not been studied how much more expressive this second class of models is. In this pap...

A Chain Event Graph (CEG) is a graphial model which designed to embody conditional independencies in problems whose state spaces are highly asymmetric and do not admit a natural product structure. In this paer we present a probability propagation algorithm which uses the topology of the CEG to build a transporter CEG. Intriungly,the transporter CEG is directly analogous to the triangulated Baye...

A chain graph (CG) is a graph admitting both directed and undirected edges with forbidden directed cycles. It generalizes both the concept of undirected graph (UG) and the concept of directed acyclic graph (DAG). CGs can be used eeciently to store graphoids, that is, independency knowledge of the form \X is independent of Y given Z" obeying a set of ve properties (axioms). Two equivalent criter...

Andersson-Madigan-Perlman chain graphs were originally introduced to represent independence models. They have recently been shown to be suitable for representing causal models with additive noise. In this paper, we present an algorithm for learning causal chain graphs. The algorithm builds on the ideas by Hoyer et al. (2009), i.e. it exploits the nonlinearities in the data to identify the direc...

There are six classes of endomorphisms for a graph. The sets these form chain under the inclusion sets. In order to systematically study endomorphisms, Böttcher and Knauer defined concepts endomorphism spectrum type graph in 1992. this paper, based on property structure monoids graphs, double-edge fan graphs described. particular, we give spectra types graphs.

Markov Chain Monte Carlo algorithms are often used to sample combinatorial structures such as matchings and independent sets in graphs. A Markov chain is defined whose state space includes the desired sample space, and which has an appropriate stationary distribution. By simulating the chain for a sufficiently large number of steps, we can sample from a distribution arbitrarily close to the sta...

We show that the switch Markov chain for sampling simple undirected, as well as bipartite, graphs with a given degree sequence is rapidly mixing when the degree sequence is strongly stable. Strong stability is closely related to the notion of P-stability introduced by Jerrum and Sinclair (1990), and is satisfied by all degree sequences for which the switch chain is known to be rapidly mixing ba...