‎Let $ \sum_{i=0}^{n}(-1)^il_ix^{n-i}$ and $\sum_{i=0}^{n}(-1)^iq_ix^{n-i}$ be the characteristic polynomials of the Laplacian matrix and signless Laplacian matrix of an $n$-vertex graph‎, ‎respectively‎. ‎Let $\alpha_i = ...

‎The second multiplicative Zagreb eccentricity index $E^{*}_{2} ({G})$ of a simple connected‎ graph $G$ is expressed as the product of the weights‎ $\varepsilon_{G}(a)\varepsilon_{G}(b)$ over all edges $ab$ of $G$‎, where ...

‎The number of spanning trees of a graph $G$ is called the complexity of $G$‎. It is known that the complexity of the line graph of a given graph $G$ can‎ be computed as the sum over all spanning trees of $G$ of contributions‎ ...

‎The Sombor index $(SO)$ is a recently invented vertex-degree-based molecular structure-descriptor‎. ‎Let $M_1$ be the first Zagreb index‎. ‎The fact that $SO$ is bounded from below by $M_{1}/\sqrt{2}$ and from above by ...