arXiv subjects

Jiaxiang Yang

Publications and source records attributed to Jiaxiang Yang.

4 recordsLinked to original sources

arXiv2022

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.

math.CO↗

arXiv2022

Maximum first Zagreb index of orientations of unicyclic graphs with given matching number

Let $D=(V,A)$ be a digraphs without isolated vertices. The first Zagreb index of a digraph $D$ defined as a summation over all arcs, $M_1(D)=\frac{1}{2}\sum\limits_{uv\in A}(d^{+}_{u}+d^{-}_v)$, where $d^{+}_u$(resp. $d^{-}_u$) denotes the out-degree (resp. in-degree) of the vertex $u$. In this paper, we give the maximal values and maximal digraphs of first Zagreb index over the set of all orientations of unicyclic graphs with $n$ vertices and matching number $m$ $(2\leq m\leq \lfloor \frac{n}{2}\rfloor)$.

math.CO↗

arXiv2022

Maximum zeroth-order general Randić index of orientations of cacti

The zeroth-order general Randić index $R^{0}_{a+1}$ of an $n$-vertices oriented graph $D$ is equal to the sum of $(d^{+}_{u_i})^{a}+(d^{-}_{u_j})^{a}$ over all arcs $u_iu_j$ of $D$, where we denote by $d^{+}_{u_i}$ the out-degree of the vertex $u_i$ and $d^{-}_{u_j}$ the in-degree of the vertex $u_j$, $a$ is an arbitrary real number. In the paper, we determine the orientations of cacti with the maximum value of the zeroth-order general Randić index for $a\geq 1$.

math.GM↗

arXiv2021

On the vertex-degree based invariants of digraphs

Let $D=(V,A)$ be a digraphs without isolated vertices. A vertex-degree based invariant $I(D)$ related to a real function $φ$ of $D$ is defined as a summation over all arcs, $I(D) = \frac{1}{2}\sum_{uv\in A}{φ(d_u^+,d_v^-)}$, where $d_u^+$ (resp. $d_u^-$) denotes the out-degree (resp. in-degree) of a vertex $u$. In this paper, we give the extremal values and extremal digraphs of $I(D)$ over all digraphs with $n$ non-isolated vertices. Applying these results, we obtain the extremal values of some vertex-degree based topological indices of digraphs, such as the Randić index, the Zagreb index, the sum-connectivity index, the $GA$ index, the $ABC$ index and the harmonic index, and the corresponding extremal digraphs.

math.CO↗