Tuning Lithiophilicity and Stability of 3D Conductive Scaffold via Covalent Ag-S Bond for High-Performance Lithium Metal Anode

Li metal anode holds great promise to realize high-energy battery systems.However,the safety issue and limited lifetime caused by the uncontrollable growth of Li dendrites hinder its commercial application.Herein,an interlayer-bridged 3D lithiophilic rGO-Ag-S-CNT composite is proposed to guide uniform and stable Li plating/stripping.The 3D lithiophilic rGO-Ag-S-CNT host is fabricated by incorporating Ag-modified reduced graphene oxide(rGO)with S-doped carbon nanotube(CNT),where the rGO and CNT are closely connected via robust Ag-S covalent bond.This strong Ag-S bond could enhance the structural stability and electrical connection between rGO and CNT,significantly improving the electrochemical kinetics and uniformity of current distribution.Moreover,density functional theory calculation indicates that the introduction of Ag-S bond could further boost the binding energy between Ag and Li,which promotes homogeneous Li nucleation and growth.Consequently,the rGO-Ag-S-CNT-based anode achieves a lower overpotential(7.3 mV at 0.5 mA cm^(−2)),higher Coulombic efficiency(98.1%at 0.5 mA cm^(−2)),and superior long cycling performance(over 500 cycles at 2 mA cm−2)as compared with the rGO-Ag-CNT-and rGO-CNT-based anodes.This work provides a universal avenue and guidance to build a robust Li metal host via constructing a strong covalent bond,effectively suppressing the Li dendrites growth to prompt the development of Li metal battery.

Extremality of Graph Entropy Based on Degrees of Uniform Hypergraphs with Few Edges

Let Η be a hypergraph with n vertices. Suppose that di,￠/2,...,dn are degrees of the vert ices of Η. The t-th graph entropy based on degrees of H is defined as Id^t(Η)=-n∑i=1(di^t/∑j=1^ndj^t^nlogdi^t/∑j=1^ndj^t^n)=log(n∑i=1di^t)-n∑i=1(di^t/∑j=1^ndj^tlogdi^t), where t is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of Id^t(Η) for t = 1, when Η is among all uniform super trees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.

Bounds for the Rainbow Disconnection Numbers of Graphs

An edge-cut of an edge-colored connected graph is called a rainbow cut if no two edges in the edge-cut are colored the same.An edge-colored graph is rainbow disconnected if for any two distinct vertices u and v of the graph,there exists a rainbow cut separating u and v.For a connected graph G,the rainbow disconnection number of G,denoted by rd(G),is defined as the smallest number of colors required to make G rainbow disconnected.In this paper,we first give some upper bounds for rd(G),and moreover,we completely characterize the graphs which meet the upper bounds of the NordhausGaddum type result obtained early by us.Secondly,we propose a conjecture that for any connected graph G,either rd(G)=λ^(+)(G)or rd(G)=λ^(+)(G)+1,whereλ^(+)(G)is the upper edge-connectivity,and prove that the conjecture holds for many classes of graphs,which supports this conjecture.Moreover,we prove that for an odd integer k,if G is a k-edge-connected k-regular graph,thenχ’(G)=k if and only if rd(G)=k.It implies that there are infinitely many k-edge-connected k-regular graphs G for which rd(G)=λ^(+)(G)for odd k,and also there are infinitely many k-edge-connected k-regular graphs G for which rd(G)=λ^(+)(G)+1 for odd k.For k=3,the result gives rise to an interesting result,which is equivalent to the famous Four-Color Problem.Finally,we give the relationship between rd(G)of a graph G and the rainbow vertex-disconnection number rvd(L(G))of the line graph L(G)of G.

The Rainbow Vertex-disconnection in Graphs

Let G be a nontrivial connected and vertex-colored graph. A subset X of the vertex set of G is called rainbow if any two vertices in X have distinct colors. The graph G is called rainbow vertex-disconnected if for any two vertices x and y of G, there exists a vertex subset S of G such that when x and y are nonadjacent, S is rainbow and x and y belong to different components of G-S;whereas when x and y are adjacent, S + x or S + y is rainbow and x and y belong to different components of(G-xy)-S. For a connected graph G, the rainbow vertex-disconnection number of G, denoted by rvd(G), is the minimum number of colors that are needed to make G rainbow vertexdisconnected. In this paper, we characterize all graphs of order n with rainbow vertex-disconnection number k for k ∈ {1, 2, n}, and determine the rainbow vertex-disconnection numbers of some special graphs. Moreover, we study the extremal problems on the number of edges of a connected graph G with order n and rvd(G) = k for given integers k and n with 1 ≤ k ≤ n.