arXiv subjects

Wei Jin

Publications and source records attributed to Wei Jin.

114 records · Page 7Linked to original sources

arXiv2015

Finite 2-distance transitive graphs

A non-complete graph $Γ$ is said to be $(G,2)$-distance transitive if $G$ is a subgroup of the automorphism group of $Γ$ that is transitive on the vertex set of $Γ$, and for any vertex $u$ of $Γ$, the stabilizer $G_u$ is transitive on the sets of vertices at distance 1 and 2 from $u$. This paper investigates the family of $(G,2)$-distance transitive graphs that are not $(G,2)$-arc transitive. Our main result is the classification of such graphs of valency not greater than 5.

math.GR↗

arXiv2015

Finite 2-geodesic transitive graphs of prime valency

We classify non-complete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of $2$-geodesics. We prove that either $Γ$ is 2-arc transitive or the valency $p$ satisfies $p\equiv 1\pmod 4$, and for each such prime there is a unique graph with this property: it is a non-bipartite antipodal double cover of the complete graph $K_{p+1}$ with automorphism group $PSL(2,p)\times Z_2$ and diameter 3.

math.CO↗

arXiv2014

On Enriching the Levin-Wen model with Symmetry

Symmetry protected and symmetry enriched topological phases of matter are of great interest in condensed matter physics due to new materials such as topological insulators. The Levin-Wen model for spin/boson systems is an important rigorously solvable model for studying $2D$ topological phases. The input data for the Levin-Wen model is a unitary fusion category, but the same model also works for unitary multi-fusion categories. In this paper, we provide the details for this extension of the Levin-Wen model, and show that the extended Levin-Wen model is a natural playground for the theoretical study of symmetry protected and symmetry enriched topological phases of matter.

cond-mat.str-el↗

arXiv2014

Improving Efficiency and Scalability of Formula-based Debugging

Formula-based debugging techniques are becoming increasingly popular, as they provide a principled way to identify potentially faulty statements together with information that can help fix such statements. Although effective, these approaches are computationally expensive, which limits their practical applicability. Moreover, they tend to focus on failing test cases alone, thus ignoring the wealth of information provided by passing tests. To mitigate these issues, we propose two techniques: on-demand formula computation (OFC) and clause weighting (CW). OFC improves the overall efficiency of formula-based debugging by exploring all and only the parts of a program that are relevant to a failure. CW improves the accuracy of formula-based debugging by leveraging statistical fault-localization information that accounts for passing tests. Our empirical results show that both techniques are effective and can improve the state of the art in formula-based debugging.

cs.SE↗

arXiv2012

Line graphs and $2$-geodesic transitivity

For a graph $Γ$, a positive integer $s$ and a subgroup $G\leq \Aut(Γ)$, we prove that $G$ is transitive on the set of $s$-arcs of $Γ$ if and only if $Γ$ has girth at least $2(s-1)$ and $G$ is transitive on the set of $(s-1)$-geodesics of its line graph. As applications, we first prove that the only non-complete locally cyclic $2$-geodesic transitive graphs are the complete multipartite graph $K_{3[2]}$ and the icosahedron. Secondly we classify 2-geodesic transitive graphs of valency 4 and girth 3, and determine which of them are geodesic transitive.

math.CO↗

arXiv2011

On distance, geodesic and arc transitivity of graphs

We compare three transitivity properties of finite graphs, namely, for a positive integer $s$, $s$-distance transitivity, $s$-geodesic transitivity and $s$-arc transitivity. It is known that if a finite graph is $s$-arc transitive but not $(s+1)$-arc transitive then $s\leq 7$ and $s\neq 6$. We show that there are infinitely many geodesic transitive graphs with this property for each of these values of $s$, and that these graphs can have arbitrarily large diameter if and only if $1\leq s\leq 3$. Moreover, for a prime $p$ we prove that there exists a graph of valency $p$ that is 2-geodesic transitive but not 2-arc transitive if and only if $p\equiv 1\pmod 4$, and for each such prime there is a unique graph with this property: it is an antipodal double cover of the complete graph $K_{p+1}$ and is geodesic transitive with automorphism group $PSL(2,p)\times Z_2$.

math.CO↗