Related papers: On the Irregularity of Some Molecular Structures
A matchstick graph is a planar unit-distance graph. We call it \emph{4-regular} if every vertex has degree 4. While examples of 4-regular matchstick graphs with fewer than 63 vertices are known only for $n \in \{52, 54, 57, 60\}$, we prove…
The Wiener index is one of the oldest graph parameter which is used to study molecular-graph-based structure. This parameter was first proposed by Harold Wiener in 1947 to determining the boiling point of paraffin. The Wiener index of a…
In chemical graph theory, caterpillar trees have been an appealing model to represent the molecular structures of benzenoid hydrocarbon. Meanwhile, topological index has been thought of as a powerful tool for modeling quantitative…
Very recently, the first geometric-arithmetic index $GA$ and arithmetic-geometric index $AG$ were introduced in mathematical chemistry. In the present paper, we first obtain some lower and upper bounds on $AG$ and characterize the extremal…
Does the intrinsic curvature of complex networks hold the key to unveiling graph anomalies that conventional approaches overlook? Reconstruction-based graph anomaly detection (GAD) methods overlook such geometric outliers, focusing only on…
We present a systematic study of the regularity phenomena for NIP hypergraphs and connections to the theory of (locally) generically stable measures, providing a model-theoretic hypergraph version of the results from [L. Lov\'asz, B.…
Parity violating elastic electron-nucleus scattering provides an accurate and model independent measurement of neutron densities, because the $Z^0$ couples primarily to neutrons. Coulomb distortion corrections to the parity violating…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
We introduce a notion of curvature on finite, combinatorial graphs. It can be easily computed by solving a linear system of equations. We show that graphs with curvature bounded below by $K>0$ have diameter bounded by $\mbox{diam}(G) \leq…
A key concept for many graph layout algorithms is planarity, a graph property that allows to draw vertices and edges crossing-free in the plane. Important is the generalization to $k$-planar graphs, which can be drawn in the plane with at…
Highlights of ATLAS and CMS measurements involving the production of heavy electroweak gauge bosons, W and Z, at the LHC are presented. Cross sections of single W and Z bosons are studied with very high precision and differential in various…
Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
We consider the electroweak production of a top quark in association with a photon at the LHC to probe the electroweak top quark couplings (t$\bar{\text{t}}\gamma$) as well as the triple gauge boson couplings (WW$\gamma$). The study is…
This book presents a comprehensive and systematic survey of graph theory under uncertainty, with particular emphasis on the unifying role of the uncertain graph framework. It reviews fundamental concepts, structural properties, graph…
Quantum transport properties of disordered graphene with structural defects (Stone-Wales and divacancies) are investigated using a realistic {\pi}-{\pi}* tight-binding model elaborated from ab initio calculations. Mean free paths and…
A 4-regular matchstick graph is a planar unit-distance graph whose vertices have all degree 4. Examples of 4-regular matchstick graphs are currently known for all number of vertices $\geq$ 52 except for 53, 55, 56, 58, 59, 61, and 62. In…
Recent measurements of multiboson production from the CMS experiment will be presented, as well as limits on anomalous triple and quartic gauge couplings. Precision measurements of multiboson production allow a basic test of the Standard…
The natural measure in a map with type-III intermittent chaos is used to define critical exponents for the average of a variable from a dynamical system near bifurcation. Numerical experiments were done with maps and verify the analytical…
We report a facile `metric' for the identification of structurally and dynamically (positive definite phonon structure) stable inorganic compounds. The metric considers charge-imbalance within the local substructures in crystalline…