A dominating set S of a graph , is subset the vertex V (G) such that any not in adjacent to at least one .The domination number G denoted by minimum size sets G. In this paper we introduced numbers certain prism graphs.

The bond strength between enamel and resin depends on achieving an etching pattern on the enamel surface which allows the resin to penetrate into the enamel and form tags. Silverstone et al. (1975) have described three basic etching patterns of human dental enamel using phosphoric acid solution. Type I etching pattern is related to the removal of the prism core material with the prism peripheri...

Human subjects threw balls of clay at a visual target while looking through wedge prism spectacles. In studies of short-term adjustment, subjects threw in the direction of their prism-bent gaze, missing the target to that side. Within 10-30 throws, they gradually adapted with a wider gaze-throw angle and hit the target. Immediately after removal of the prisms the wide gaze-throw angle persisted...

 In this paper, we introduce a suitable generalization of Cayley graphs that is defined over polygroups (GCP-graph) and give some examples and properties. Then, we mention a generalization of NEPS that contains some known graph operations and apply to GCP-graphs. Finally, we prove that the product of GCP-graphs is again a GCP-graph.

The 3-polytopes are planar, 3-connected graphs. A classical question is, given r≥3, is the 2(r−1)-gonal prism K2×C2(r−1) unique 3-polytope of graph radius r and smallest size? Under some extra assumptions, we answer this in positive.

The following problem was posed by C.A. Nicol: given any finite sequence of positive integers, find the permutation for which the continuant (i.e. the continued fraction denominator) having these entries is maximal, resp. minimal. The extremal arrangements are known for the regular continued fraction expansion. For the singular expansion induced by the backward shift d1/xe − 1/x the problem is ...

Probabilistic model checking is a formal verification technique for establishing the correctness, performance and reliability of systems which exhibit stochastic behaviour. As in conventional verification, a precise mathematical model of a real-life system is constructed first, and, given formal specifications of one or more properties of this system, an analysis of these properties is performe...

We propose to study the problem of few-shot learning with the prism of inference on a partially observed graphical model, constructed from a collection of input images whose label can be either observed or not. By assimilating generic message-passing inference algorithms with their neural-network counterparts, we define a graph neural network architecture that generalizes several of the recentl...

In this paper, we are studying vertex-magic total labelings of simple graphs. We introduce a procedure called mutation which transforms one labeling into another by swapping sets of edges among vertices. The result of a mutation may be a different labeling of the same graph or a labeling of a different graph. Mutation proves to be a remarkably fruitful process— for example we are able to genera...

We propose to study the problem of few-shot learning with the prism of inference on a partially observed graphical model, constructed from a collection of input images whose label can be either observed or not. By assimilating generic message-passing inference algorithms with their neural-network counterparts, we define a graph neural network architecture that generalizes several of the recentl...