Related papers: Weakly distance-regular digraphs of diameter 2
In this paper, we study commutative weakly distance-regular digraphs whose attached association schemes are regular, and give a characterization of mixed arcs. As an application, we classify such digraphs of diameter 2.
Weakly distance-regular digraphs are a natural directed version of distance-regular graphs. In [8], the third author and Suzuki proposed a question when an orientation of a distance-regular graph defines a weakly distance-regular digraph.…
Weakly distance-regular digraphs are a natural directed version of distance-regular graphs. In [16], we classified all commutative weakly distance-regular digraphs whose underlying graphs are Hamming graphs, folded n-cubes, or Doob graphs.…
A weakly distance-regular digraph is $P$-polynomial if its attached scheme is $P$-polynomial. In this paper, we characterize all $P$-polynomial weakly distance-regular digraphs.
In this paper, we classify commutative weakly distance-regular digraphs of valency 3 with girth more than 2 and one type of arcs. Combining [8, Theorem 1.2], [10, Theorem 1.3] and [11, Theorem 1], commutative weakly distanceregular digraphs…
A weakly distance-regular digraph is quasi-thin if the maximum value of its intersection numbers is 2. In this paper, we focus on commutative quasi-thin weakly distance-regular digraphs, and classify such digraphs with valency more than 3.…
A weakly distance-regular digraph is thick if its attached scheme is regular. In this paper, we show that each commutative thick weakly distance-regular digraph has a thick weakly distance-regular subdigraph such that the corresponding…
In this paper, we classify all commutative weakly distance-regular digraphs of girth $g$ and one type of arcs under the assumption that $p_{(1,g-1),(1,g-1)}^{(2,g-2)}\geq k_{1,g-1}-2$. In consequence, we recover [13, Theorem 1.1] as a…
A weakly distance-regular digraph is quasi-thin if the maximum value of its intersection numbers is 2. In this paper, we show that the valency of any commutative quasi-thin weakly distance-regular digraph is at most 6.
A weakly distance-regular digraph is 3-equivalenced if its attached association scheme is 3-equivalenced. In this paper, we classify the family of such digraphs under the assumption of the commutativity.
Suzuki (2004) [7] classified thin weakly distance-regular digraphs and pro- posed the project to classify weakly distance-regular digraphs of valency 3. The case of girth 2 was classified by the third author (2004) [9] under the assumption…
We classify certain non-symmetric commutative association schemes. As an application, we determine all the primitive weakly distance-regular circulant digraphs.
We classify the distance-regular Cayley graphs with least eigenvalue $-2$ and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain…
A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer $m\geq 2$, there are only finitely many…
Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavi\v{c} and Poto\v{c}nik proposed the problem of charaterizing distance-regular Cayley graphs, which can be viewed as a natural…
Using the two way distance, we introduce the concepts of weak metric dimension of a strongly connected digraph $\Gamma$. We first establish lower and upper bounds for the number of arcs in $\Gamma$ by using the diameter and weak metric…
A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood (resp. in-neighbourhood) of any vertex induces a semicomplete digraph. In this paper, we characterize all…
In this paper, we introduce the notion of the weak majority dimension of a digraph which is well-defined for any digraph. We first study properties shared by the weak dimension of a digraph and show that a weak majority dimension of a…
In this paper, we give a characterization of distance matrices of distance-regular graphs to be invertible.
We determine the distance-regular graphs with diameter at least $3$ and $c_2\geq 2$ but without induced $K_{1,4}$-subgraphs.