Let G = (V (G), E(G)) be a finite simple graph without loops. The neighbourhood N (v) of a vertex v is the set of vertices adjacent to v. The degree d(v) of v is |N (v)|. The minimum and maximum degree of G are denoted by δ(G) and 1(G), respectively. For a vertex v ∈ V (G) and a subset S ⊆ V (G), NS(v) is the set of neighbours of v contained in S, i.e., NS(v) = N (v) ∩ S. We let dS(v) = |NS(v)|...

A graph G is said to be cyclable if for each orientation → G of G, there exists a set S of vertices such that reversing all the arcs of → G with one end in S results in a hamiltonian digraph. Let G be a 3-connected graph of order n¿ 36. In this paper, we show that if for any three independent vertices x1, x2 and x3, |N (x1) ∪ N (x2)|+ |N (x2) ∪ N (x3)|+ |N (x3) ∪ N (x1)|¿ 2n+ 1, then G is cycla...

Graphene-wrapped FeF3 nanocrystals (FeF3/G) have been successfully fabricated for the first time by a vapour-solid method, which can be generalized to synthesize other metal fluorides. The as-synthesized FeF3/G delivers a charge capacity of 155, 113, and 73 mA h g(-1) at 104, 502, and 1040 mA g(-1) in turn, displaying superior rate capability to bare FeF3. Moreover, it exhibits stable cyclabili...

Multiwall carbon nanotubes (CNTs) were synthesized by catalytic chemical vapor deposition of acetylene and used as templates to prepare CNT-Sb and CNT-SnSb0.5 nanocomposites via the chemical reduction of SnCl2 and SbCl3 precursors. SEM and TEM imagings show that the Sb and SnSb0.5 particles were uniformly dispersed in the CNT web and on the outside surface of CNTs. These CNT-metal composites ar...

Thermochemical energy storage materials and reactors have been reviewed for a range of temperature applications. For low-temperature applications, magnesium chloride is found to be suitable candidate at temperatures up 100 °C, whereas calcium hydroxide identified appropriate medium-temperature ranging from 400 °C 650 °C. the high-temperature (750–1050 °C), oxides cobalt, manganese, copper are r...

A mechanically strong binder with polar functional groups could overcome the dilemma of large volume change during charge/discharge processes and poor cyclability lithium-sulfur batteries (LSBs). In this work, for first time, we report use poly(thiourea triethylene glycol) (PTTG) as a multifunctional sulfur cathodes to enhance performance LSBs. As expected, PTTG facilitates high stability deliv...