2 citations · 3 across the 10 of their papers we have counts for
12 papers · 1 filter
A proof of the resistance diameter conjecture for line graphs
Xiang-Feng Pan, Xiang-Yang Liu, Zhen-Mu Hong
We prove the conjecture of Xu, Li, Hua, and Pan that the resistance diameter does not increase under the line-graph operation. For every finite connected simple graph with at l…
Sharp upper bounds on the -spectral radius of graphs
Zhen-Mu Hong, Zheng-Jiang Xia, Zhi Qiao
Let be a simple graph with degree diagonal matrix and adjacency matrix . The signless Laplacian matrix of is defined as . For a real number $α\…
Characterization of the structure of -edge-maximal graphs
Zheng-Jiang Xia, Hong-Jian Lai, Jian Lu +1
Let be the edge-connectivity of the graph . The \textit{strength} of , denoted by , is the maximum edge-connectivity of its subgraphs.…
On the disjunctive domination numbers of the torus grid graphs
Zhi Qiao, Zheng-Jiang Xia, Zhen-Mu Hong
Let be a graph. The disjunctive domination number of is the minimum cardinality of a set such that every vertex not in is adjacent to a vertex of $…
Connectivity and eigenvalues of graphs with given girth or clique number
Zhen-Mu Hong, Hong-Jian Lai, Zheng-Jiang Xia
Let , , and denote the edge-connectivity, vertex-connectivity, the algebraic connectivity and the Laplacian spectral radius of , respectively.…
Induced subgraphs of product graphs and a generalization of Huang's theorem
Zhen-Mu Hong, Hong-Jian Lai, Jian-Bing Liu
Recently, Huang showed that every -vertex induced subgraph of the -dimensional hypercube has maximum degree at least in [Annals of Mathematics, 190 (2019…
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…
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 -pebbling number of a graph is the minimum number…
Sufficient conditions for graphs to be -connected, maximally connected and super-connected
Zhen-Mu Hong, Zheng-Jiang Xia, Fuyuan Chen +1
Let be a connected graph with minimum degree and vertex-connectivity . The graph is -connected if , maximally connected if , and su…
Pebbling on Jahangir graphs
Zheng-Jiang Xia, Zhen-Mu Hong, Fu-Yuan Chen
The pebbling number of a graph , , is the least such that, however pebbles are placed on the vertices of , we can move a pebble to any vertex by a sequence of m…
On restricted edge-connectivity of replacement product graphs
Zhen-Mu Hong, Jun-Ming Xu
This paper considers the edge-connectivity and restricted edge-connectivity of replacement product graphs, gives some bounds on edge-connectivity and restricted edge-connectivity o…
Vulnerability of super edge-connected graphs
Zhen-Mu Hong, Jun-Ming Xu
A subset of edges in a connected graph is a -extra edge-cut if is disconnected and every component has more than vertices. The -extra edge-connectivity $\la…