A cubical Feynman category, introduced by the authors in previous work, is a category whose functors to base C <mml:annotation encoding="appl...

We present a general method to improve computation of answer sets by analyzing structural properties of normal logic programs. Therefore we use labeled directed graphs associated to normal programs, which can be utilized to compute answer sets. The basic idea is to detect special subgraphs of those graphs corresponding to structural properties of normal programs and transform them into simpler ...

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

We present a linear time algorithm for testing clustered planarity of c-connected clustered graphs and for computing a clustered planar embedding for such graphs. Our algorithm uses a decomposition of the input graph based on SPQR-trees and is the first linear time algorithm for clustered planarity testing. We define a normal form of clustered embeddings and show that a clustered graph is clust...

We derive normal approximation bounds in the Wasserstein distance for sums of generalized U-statistics, based on a general bound functionals independent random variables arbitrary distributions. Those are applied to combined weights subgraphs Erdős–Rényi graph, extending graph counting results Barbour et al. (A central limit theorem decomposable with applications graphs, J. Combin. Theory Ser. ...

Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.

Molecular descriptors are a basic tool in the spectral graph, molecular chemistry, and various other fields of mathematics chemistry. Kulli–Basava K mathvariant="fraktur">B indices were initiated for chemical applicatio...

FOX-7 (1,1-diamino-2,2-dinitroethylene) recently is expected as a relatively new energetic material with high-performance and low sensitivity. The RHF and MP2 levels and DFT method with B3LYP functional with aug-cc-pVDZ basis set have been used for obtaining equilibrium geometry and Rho function (electron density distribution). By the aid of fundamental physical theorems implemented in the ...

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.