Somayeh Shafiee Alamoti

arXiv2024

On Thermodynamic Properties of Circumacenes Through Zagreb Indices

We explore the fascinating world of Circumacenes, a unique family of organic molecules. Our research demonstrarates the calculation of essential topological indices, including the first and second-Zagreb indices, as well as related generalized indices, and their relationship with the structure of these molecules. We also indicate how these indices can help predict crucial thermodynamic properties, such as gap energy and electron affinity energy, using an innovative method called the Topological Indices Method (TIM).

physics.chem-ph↗

arXiv2024

Edge Quasi $λ$-distance-balanced Graphs in Metric Space

In a graph $A$, the measure $|M_g^A(f)|=m_g^A(f)$ for each arbitrary edge $f=gh$ counts the edges in $A$ closer to $g$ than $h$. $A$ is termed an edge quasi-$λ$-distance-balanced graph in a metric space (abbreviated as $EQDBG$), where a rational number ($>1$) is assigned to each edge $f=gh$ such that $m_g^A(f)=λ^{\pm1}m_h^A(f)$. This paper introduces and discusses these graph concepts, providing essential examples and construction methods. The study examines how every $EQDBG$ is a bipartite graph and calculates the edge-Szeged index for such graphs. Additionally, it explores their properties in Cartesian and lexicographic products. Lastly, the concept is extended to nicely edge distance-balanced and strongly edge distance-balanced graphs revealing significant outcomes.

math.CO↗