A note on the minimum reduced reciprocal Randić index of n-vertex unicyclic graphs

Maximum zeroth-order general Randić index of orientations of trees, unicyclic and bicyclic graphs with given matching number

The zeroth-order general Randić index $R^{0}_{a}$ of a digraph $D$ is the sum of $(d^{+}_{v})^{a}+(d^{-}_{w})^{a}$ over all arcs $vw$ of $D$, where $a$, $d^{+}_{v}$ and $d^{-}_{w}$ are an arbitrary real number, the out-degree of the vertex $v$ and the in-degree of the vertex $w$, respectively. We determine maximum zeroth-order general Randić index of oriented trees, unicyclic and bicyclic graphs in terms of matching number and order in this paper.

Construction of equienergetic and Randic' equienergetic graphs

In this paper, we give several constructions for the pairs of graphs to be equienergetic and Randic' equienergetic graphs. Also, some new families of integral and Randic' integral graphs are obtained. As an application, a sequence of graphs established with reciprocal eigenvalue property and anti-reciprocal eigenvalue property.

Maximum reciprocal degree resistance distance index of unicyclic graphs

The reciprocal degree resistance distance index of a connected graph $G$ is defined as $RDR(G)=\sum\limits_{\{u,v\}\subseteq V(G)}\frac {d_G(u)+d_G(v)}{r_G(u,v)}$, where $r_G(u,v)$ is the resistance distance between vertices $u$ and $v$ in $G$. Let $\mathscr {U}_n$ denote the set of unicyclic graphs with $n$ vertices. We study the graph with maximum reciprocal degree resistance distance index among all graphs in $\mathscr {U}_n$, and characterize the corresponding extremal graph.

The minimum ABS index of trees with given number of pendent vertices

The recently developed atom-bond sum-connection (ABS) index is a variation of the well-studied graph-based molecular descriptors connectivity (Randic), atom-bond connectivity, and sum-connectivity indices.We present the minimum ABS index of trees with a given number of pendent vertices in this paper, which provides a solution to the problem proposed by A. Ali, I. Gutman and I. Redzepovic, Atom-Bond Sum-Connectivity Index of Unicyclic Graphs and Some Applications, Electron. J. Math.(2023) 1-7

ChemicHull: 一种用于确定最大度数不超过3的极值化学图的在线工具

ChemicHull: an online tool for determining extremal chemical graphs of maximum degree at most 3 for any degree-based topological indices

ChemicHull是一种在线工具，用于确定任意度数基于拓扑指数的极值化学图，通过线性优化在多面体框架内分析化学图的极值特性。