Restricted detour distance between two vertices and of a graph is the length longest u- v path for induced condition (V (P))=P. The restricted polynomial depends on denoted by D*(G,x) defined = ∑{u,v}xD*(u,v) where summation taken over all unordered pairs (u,v) distinct u V(G). In this paper, we investigate straight chain wheel graphs φ(WkB) compute index φ(WkB).

Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of ...

Mahlmann and Schindelhauer (2005) defined a Markov chain which they called kFlipper, and showed that it is irreducible on the set of all connected regular graphs of a given degree (at least 3). We study the 1-Flipper chain, which we call the flip chain, and prove that the flip chain converges rapidly to the uniform distribution over connected 2r-regular graphs with n vertices, where n ≥ 8 and r...

We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although it is known that this can be achieved in polynomial time for any graph, the algorithm studied here is more natural in the context of planar Eulerian graphs. We analyse the mixing time of a Markov chain on the Eulerian orientations of a planar gra...

The paper gives a few arguments in favour of use of chain graphs for description of proba­ bilistic conditional independence structures. Every Bayesian network model can be equiva­ lently introduced by means of a factorization formula with respect to chain graph which is Markov equivalent to the Bayesian network. A graphical characterization of such graphs is given. The class of equivalent grap...

Let 1 ≤ n ∈ Z. Worst-case efficient dominating sets in digraphs are conceived so that their presence in certain strong digraphs ~ STn corresponds to that of efficient dominating sets in star graphs STn: The fact that the star graphs STn form a so-called dense segmental neighborly E-chain is reflected in a corresponding fact for the digraphs ~ STn. Related chains of graphs and open problems are ...

The ability to simulate graphs with given properties is important for the analysis of social networks. Sequential importance sampling has been shown to be particularly effective in estimating the number of graphs adhering to fixed marginals and in estimating the null distribution of graph statistics. This paper describes the networksis package for R and how its simulate and simulate_sis functio...

Depending on the interpretation of the type of edges, a chain graph can represent different relations between variables and thereby independence models. Three interpretations, known by the acronyms LWF, MVR, and AMP, are prevalent. Multivariate regression (MVR) chain graphs were introduced by Cox and Wermuth in 1993. We review Markov properties for MVR chain graphs chronologically, and for the ...

While some software engineering applications perform static analysis over the whole program call graph, others are more interested in specific call chains within a program’s call graph. It is thus important to identify when a particular static call chain for an object-oriented program may not be executable, or feasible, such that there is no input for which the chain will be taken. This paper e...

We define cooperative games on general graphs and generalize Lloyd S. Shapley's celebrated allocation formula for those in terms of stochastic path integral driven by the associated Markov chain each graph. then show that value operator, one player defined integral, coincides with player's component game which is solution to least squares (or Poisson's) equation, light combinatorial Hodge decom...