The expected subtree number index in random polyphenylene and spiro chains

The number of maximal matchings in polyphenylene chains

A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also de...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the n...

expected number of local maxima of some gaussian random polnomials

The Expected Number of Missing Words in a Random Text

The number of words of length q (q-grams) in a text or the number of common q-grams between two texts are used in pattern matching algorithms, as distance measure between texts or for testing the randomness of pseudorandom number generators. Despite this broad range of applications, no exact systematic statistical studies of those numbers can be found in the literature. We propose an algorithm ...