Jianguo Qian

activity

20172022

collaborators

15 papers

math.CO2022

Graphs with second largest eigenvalue less than $1/2$

Xiaoxia Wu, Jianguo Qian, Haigen Peng

We characterize the simple connected graphs with the second largest eigenvalue less than 1/2, which consists of 13 classes of specific graphs. These 13 classes hint that $c_{2}\in…

math.CO2022

Menger-type connectivity of line graphs of faulty hypercubes

Huanshen Jia, Jianguo Qian

A connected graph $G$ is called strongly Menger edge connected if $G$ has min\{deg $_{G} (x)$ , deg $_{G} (y)$ \} edge-disjoint paths between any two distinct vertices $x$ and $y$ in $G$ . In…

math.CO2021

Extremal Polygonal Cacti for General Sombor Index

Jiachang Ye, Jianguo Qian

The Sombor index of a graph $G$ was recently introduced by Gutman from the geometric point of view, defined as $S O (G) = \sum_{uv \in E (G)} d (u)^{2} + d (v)^{2}$ , where $d (u)$ is the de…

math.CO2021

Hamiltonian cycles in 4-connected planar and projective planar triangulations with few 4-separators

On-Hei Solomon Lo, Jianguo Qian

Whitney proved in 1931 that every 4-connected planar triangulation is hamiltonian. Later in 1979, Hakimi, Schmeichel and Thomassen conjectured that every such triangulation on $n$ …

math.CO2020

Flips on homologous orientations of surface graphs with prescribed forbidden facial circuits

Weijuan Zhang, Jianguo Qian

Let $G$ be a graph embedded on an orientable surface. Given a class $C$ of facial circuits of $G$ as a forbidden class, we give a sufficient-necessary condition for that an…

math.CO2020

On non-empty cross-intersecting families

Chao Shi, Peter Frankl, Jianguo Qian

Let $2^{[n]}$ and $(i [ n ])$ be the power set and the class of all $i$ -subsets of ${1, 2, \dots, n}$ , respectively. We call two families $A$ and $B$ cross…