By using ＂pillaring＂ strategy, a new Co（Ⅱ）-MOF, [Co_2（abtc）（bimb）_2]·2H_2O（1, H_4abtc = 3,3？,5,5？-azobenzenetetracarboxylic acid, bimb = 4,4？-bis（imidazole-1-ylmethyl）biphenyl）, has been solvother...By using ＂pillaring＂ strategy, a new Co（Ⅱ）-MOF, [Co_2（abtc）（bimb）_2]·2H_2O（1, H_4abtc = 3,3？,5,5？-azobenzenetetracarboxylic acid, bimb = 4,4？-bis（imidazole-1-ylmethyl）biphenyl）, has been solvothermally synthesized and structurally characterized. The structural determination revealed that 1 features a 3D pillar-layered framework with（4,8）-connected {4^4.6^2}{4^8.6^（20）} topology based on dinuclear Co（Ⅱ）-SBUs. The magnetic investigation shows that the dominant antiferromagnetic coupling is observed in compound 1.展开更多
DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improve...DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improves the results of[Discrete Math.,2018,341(7):1983–1986]and[Discrete Appl.Math.,2020,277:245–251].展开更多
A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken ove...A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.展开更多
A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of ...A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C_4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the(combinatorial)展开更多
In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this proble...In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this problem for n sufficiently large.展开更多
基金Supported by the National Natural Science Foundation of China(Nos.21201109,21373122 and 21301106)
文摘By using ＂pillaring＂ strategy, a new Co（Ⅱ）-MOF, [Co_2（abtc）（bimb）_2]·2H_2O（1, H_4abtc = 3,3？,5,5？-azobenzenetetracarboxylic acid, bimb = 4,4？-bis（imidazole-1-ylmethyl）biphenyl）, has been solvothermally synthesized and structurally characterized. The structural determination revealed that 1 features a 3D pillar-layered framework with（4,8）-connected {4^4.6^2}{4^8.6^（20）} topology based on dinuclear Co（Ⅱ）-SBUs. The magnetic investigation shows that the dominant antiferromagnetic coupling is observed in compound 1.
基金Partially supported by NSFC(No.12301436)NSF of Guangxi Province(No.2025GXNSFAA069811)。
文摘DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improves the results of[Discrete Math.,2018,341(7):1983–1986]and[Discrete Appl.Math.,2020,277:245–251].
文摘A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.
基金Supported by the National Natural Science Foundation of China（11171273） Supported by the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical Uni- versity（Z2016170）
文摘A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C_4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the(combinatorial)
基金support from FCT—Fundacao para a Ciencia e a Tecnologia(Portugal),through Projects PTDC/MAT/113207/2009PEst-OE/MAT/UI0297/2011(CMA).
文摘In this paper we consider the problem of finding the smallest number such that any graph G of order n admits a decomposition into edge disjoint copies of C4 and single edges with at most elements. We solve this problem for n sufficiently large.
