Supported by the National Natural Science Foundation of Xinjiang(2020D04046);the National Natural Science Foundation of Shanxi(20210302123097);the National Natural Science Foundation of China(12371356,11961067).
A graph G is said to be super-connected or simply super-κ, if each minimum vertex cut of G isolates a vertex. A graph G is said to be a k-vertex-orbit graph if there are k vertex orbits when Aut(G) acts on V(G). A gr...
supported by the National Natural Science Foundation of the People's Republic of China“On disjoint path covers of graphs and related problems”(12261085);Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“On spanning wide diameter and spanning cycle ability of interconnection networks”(2021D01C116)。
A t-container Ct(u,v)is a set of t internally disjoint paths between two distinct vertices u and v in a graph G,i.e.,Ct(u,v)={P_(1),P_(2),···,Pt}.Moreover,if V(P_(1))∪V(P_(2))∪···∪V(Pt)=V(G)then Ct(u,v)is cal...
the National Natural Science Foundation of China(Nos.11971311,12161141003,and 12026230);Science and Technology Commission of Shanghai Municipality(No.22JC1403600);Li-Hua Feng and Wei-Jun Liu are partly supported by the National Natural Science Foundation of China(Nos.11871479,12071484);Hunan Provincial Natural Science Foundation(Nos.2020JJ4675,2018JJ2479).
A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted.In this paper,for a connected graph G with sufficiently large order,we pres...
We are grateful for the financial support of the National Key Research and Development Program of China(2016YFC0503200);the National Nature Science Foundation of China(31570408 and 31801986);the China Postdoctoral Science Foundation(2018M631372).
Habitat restoration is an effective method for improving landscape connectivity,which can reduce habitat fragmentation.Maintaining landscape connectivity could promote connections between habitat,which is extremely es...
supported by the National Natural Science Foundation of China(No.12071158).
Robustness of the network topology is a key aspect in the design of computer networks. Residual closeness is a new graph-theoretic concept defined as a measure of network robustness due to the failure of individual ve...
A graph G is k-triangular if each of its edge is contained in at least k triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph G is a sequen...
Supported by Tsinghua University Initiative Scientific Research Program and Project 11771246; Supported by National Natural Science Foundation of China
A subset F V(G) is called an Rk-vertex-cut of a graph G if G - F is disconnected and each vertex of G - F has at least k neighbors in G - F. The Rk-vertex-connectivity of G, denoted by κk(G), is the cardinality ...
A new lower bound on the tenacity ?of a graph G in terms of its connectivity and genus is obtained. The lower bound and interrelationship involving tenacity and other well-known graphical parameters are considered, an...
The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics. In this paper we present the explicit generalized expressions for the eccen...