Zheng-Jiang Xia

activity

20142026

most citedGraphs with many valencies and few eigenvalues

8 citations · 12 across the 12 of their papers we have counts for

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13 papers · 1 filter

math.CO2026

Sharp upper bounds on the $A_{α}$ -spectral radius of graphs

Zhen-Mu Hong, Zheng-Jiang Xia, Zhi Qiao

Let $G$ be a simple graph with degree diagonal matrix $D (G)$ and adjacency matrix $A (G)$ . The signless Laplacian matrix of $G$ is defined as $Q (G) = D (G) + A (G)$ . For a real number $α\…

math.CO2026

Characterization of the structure of $k$ -edge-maximal graphs

Zheng-Jiang Xia, Hong-Jian Lai, Jian Lu +1

Let $κ^{'} (G)$ be the edge-connectivity of the graph $G$ . The \textit{strength} of $G$ , denoted by $κ^{'} (G)$ , is the maximum edge-connectivity of its subgraphs.…

math.CO2026

On the disjunctive domination numbers of the torus grid graphs

Zhi Qiao, Zheng-Jiang Xia, Zhen-Mu Hong

Let $Γ = (V, E)$ be a graph. The disjunctive domination number of $Γ$ is the minimum cardinality of a set $S \subseteq V$ such that every vertex not in $S$ is adjacent to a vertex of $…

math.CO2022

A New Feasibility Condition for the AT4 Family

Zheng-Jiang Xia, Jae-Ho Lee, Jack H. Koolen

Let $Γ$ be an antipodal distance-regular graph with diameter $4$ and eigenvalues $θ_{0} > θ_{1} > θ_{2} > θ_{3} > θ_{4}$ . Then $Γ$ is tight in the sense of Jurišić, Koolen, and Terwilliger [12] when…

math.CO2020

Connectivity and eigenvalues of graphs with given girth or clique number

Zhen-Mu Hong, Hong-Jian Lai, Zheng-Jiang Xia

Let $κ^{'} (G)$ , $κ (G)$ , $μ_{n - 1} (G)$ and $μ_{1} (G)$ denote the edge-connectivity, vertex-connectivity, the algebraic connectivity and the Laplacian spectral radius of $G$ , respectively.…

math.CO2019

A note on the optimal rubbling in ladders and prisms

Zheng-Jiang Xia, Zhen-Mu Hong

A pebbling move on a graph G consists of the removal of two pebbles from one vertex and the placement of one pebble on an adjacent vertex. Rubbling is a version of pebbling where a…

math.CO2019

A spectral characterization of the $s$ -clique extension of the triangular graphs

Ying-Ying Tan, Jack H. Koolen, Zheng-Jiang Xia

A regular graph is co-edge regular if there exists a constant $μ$ such that any two distinct and non-adjacent vertices have exactly $μ$ common neighbors. In this paper, we show tha…

math.CO2019

Generalization of the cover pebbling number on trees

Zheng-Jiang Xia, Zhen-Mu Hong

A pebbling move on a graph consists of taking two pebbles off from one vertex and add one pebble on an adjacent vertex, the $t$ -pebbling number of a graph $G$ is the minimum number…

math.CO2017★ 2 cited

Sufficient conditions for graphs to be $k$ -connected, maximally connected and super-connected

Zhen-Mu Hong, Zheng-Jiang Xia, Fuyuan Chen +1

Let $G$ be a connected graph with minimum degree $δ (G)$ and vertex-connectivity $κ (G)$ . The graph $G$ is $k$ -connected if $κ (G) \geq k$ , maximally connected if $κ (G) = δ (G)$ , and su…

math.CO2017★ 1 cited

Graham's pebbling conjecture on Cartesian product of the middle graphs of even cycles

Zheng-Jiang Xia, Yong-Liang Pan, Jun-Ming Xu +1

A pebbling move on a graph $G$ consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The pebbling number of a graph $G$ , denoted by $f (G)$ , is the le…

math.CO2017★ 1 cited

Pebbling on Jahangir graphs

Zheng-Jiang Xia, Zhen-Mu Hong, Fu-Yuan Chen

The pebbling number of a graph $G$ , $f (G)$ , is the least $p$ such that, however $p$ pebbles are placed on the vertices of $G$ , we can move a pebble to any vertex by a sequence of m…

math.CO2014★ 8 cited

Graphs with many valencies and few eigenvalues

Edwin R. van Dam, Jack H. Koolen, Zheng-jiang Xia

Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct…

math.CO2014

Pebbling on $C_{4 k + 3} \times G$ and $M (C_{2 n}) \times G$

Zheng-Jiang Xia, Yong-Liang Pan, Jun-Ming Xu

The pebbling number of a graph $G$ , $f (G)$ , is the least $p$ such that, however $p$ pebbles are placed on the vertices of $G$ , we can move a pebble to any vertex by a sequence of m…

Sharp upper bounds on the Aα​-spectral radius of graphs

Characterization of the structure of k-edge-maximal graphs

On the disjunctive domination numbers of the torus grid graphs

A New Feasibility Condition for the AT4 Family

Connectivity and eigenvalues of graphs with given girth or clique number

A note on the optimal rubbling in ladders and prisms

A spectral characterization of the s-clique extension of the triangular graphs

Generalization of the cover pebbling number on trees

Sufficient conditions for graphs to be k-connected, maximally connected and super-connected

Graham's pebbling conjecture on Cartesian product of the middle graphs of even cycles

Pebbling on Jahangir graphs

Graphs with many valencies and few eigenvalues

Pebbling on C4k+3​×G and M(C2n​)×G

Sharp upper bounds on the $A_{α}$ -spectral radius of graphs

Characterization of the structure of $k$ -edge-maximal graphs

A spectral characterization of the $s$ -clique extension of the triangular graphs

Sufficient conditions for graphs to be $k$ -connected, maximally connected and super-connected

Pebbling on $C_{4 k + 3} \times G$ and $M (C_{2 n}) \times G$