Tetravalent edge-transitive graphs of order p 2 q

Pan, Jiangmin; Yin, Liu; Huang, Zhaohong; Liu, ChenLong

doi:10.1007/s11425-013-4708-8

Cited by 20 publications

(12 citation statements)

References 25 publications

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“…By [21], we have the following lemma regarding the tetravalent edge-transitive graph with odd but not a prime power order.…”

Section: Lemma 23 Let M Be a Soluble Maximal Subgroup Of Gl(2 P) Then M Is Isomorphic To One Of The Following Groupsmentioning

confidence: 99%

“…The tetravalent half-arc-transitive graphs of order p 3 , p 4 and 2pq are classified in [8], [9], [32], respectively. Recently, Pan et al in [21] classified tetravalent edge-transitive graphs of order p 2 q. Wang et al in [30] studied tetravalent half-arc-transitive graphs of order a product of three primes.…”

Section: Introductionmentioning

confidence: 99%

“…[21], Theorem 5.3). Let Γ be a tetravalent G-edge-transitive graph of order p 2 q, where G Aut Γ and p, q are distinct odd primes.…”

mentioning

confidence: 97%

See 2 more Smart Citations

Tetravalent half-arc-transitive graphs of order $p^2q^2$

2019

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“…By [21], we have the following lemma regarding the tetravalent edge-transitive graph with odd but not a prime power order.…”

Section: Lemma 23 Let M Be a Soluble Maximal Subgroup Of Gl(2 P) Then M Is Isomorphic To One Of The Following Groupsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tetravalent half-arc-transitive graphs of order $p^2q^2$

2019

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“…In the literature, there are lots of works in classifying symmetric graphs of order kp n and small valency d, especially with n and k small and d = 3, 4, or 5; see [6,7,12,13,24,25,27] for example. In particular, cubic or pentavalent symmetric basic graphs of order 2p n for variable prime p and integer n were classified completely in [6,7], and tetravalent 2-arc-transitive basic graphs of order 2p n were classified in [27].…”

Section: Introductionmentioning

confidence: 99%

“…As applications of above works, symmetric graphs of order 2p 2 and valency 3, 4 or 5 were determined (for valency 5, one may also refer [24]). Cubic and tetravalent symmetric graphs of order kp n for some small integer k with k > 2 were also well studied (see [4,22,25]). This paper concerns pentavalent symmetric graphs of order kp n with k > 2, and the following theorem is the main result.…”

Section: Introductionmentioning

confidence: 99%

On basic graphs of symmetric graphs of valency five

Yang¹,

Yan²,

Kwak³

et al. 2017

Preprint

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A graph Γ is symmetric or arc-transitive if its automorphism group Aut(Γ) is transitive on the arc set of the graph, and Γ is basic if Aut(Γ) has no non-trivial normal subgroup N such that the quotient graph Γ N has the same valency with Γ. In this paper, we classify symmetric basic graphs of order 2qp n and valency 5, where q < p are two primes and n is a positive integer. It is shown that such a graph is isomorphic to a family of Cayley graphs on dihedral groups of order 2q with 5 (q − 1), the complete graph K 6 of order 6, the complete bipartite graph K 5,5 of order 10, or one of the nine sporadic coset graphs associated with non-abelian simple groups. As an application, connected pentavalent symmetric graphs of order kp n for some small integers k and n are classified.

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Yolk‐Shell Structure and Spin‐Polarized Surface Capacitance Enable FeS Stable and Fast Ion Transport in Sodium‐Ion Batteries

Han,

Liu,

Deng

et al. 2024

Advanced Energy Materials

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Iron sulfide (FeS) has been extensively studied as sodium‐ion battery anodes due to its high theoretical capacity (609 mAh g−1), but its large volume expansion and low electrical conductivity result in unsatisfactory cycling life and poor rate performance. Moreover, the sodium ion storage mechanism of FeS at a voltage range of 0.01–1 V involving conversion reactions and subsequent ion storage process is unclear yet. Here, the study proposes a vapor‐pressure induced synthesis route to fabricate FeS/C yolk‐shell structure that ultrathin carbon layers coat on the surface of FeS nanosheets, which can accommodate volume expansion of FeS during sodiation observed via in situ transmission electron microscope and improve its electrical conductivity. Remarkably, an in situ magnetometry reveals that vast spin‐polarized electrons can be injected into superparamagnetic Fe nanoparticles (≈3 nm) formed during conversion reaction to induce evolution of electrode magnetization between 0.01 and 1 V, during which spin‐polarized surface capacitance effect occurs at Fe/Na2S interfaces to increase extra ion storage and boost ion transport stably. Consequently, the FeS/C yolk‐shell nanosheets deliver a high reversible capacity of 664.9 mAh g−1 at 0.1 A g−1, and 300.4 mAh g−1 after 10 000 cycles at 10 A g−1 with a capacity retention of 81.1%.

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Tetravalent edge-transitive graphs of order p 2 q

Cited by 20 publications

References 25 publications

Tetravalent half-arc-transitive graphs of order $p^2q^2$

Tetravalent half-arc-transitive graphs of order $p^2q^2$

On basic graphs of symmetric graphs of valency five

Yolk‐Shell Structure and Spin‐Polarized Surface Capacitance Enable FeS Stable and Fast Ion Transport in Sodium‐Ion Batteries

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