The notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the distance energy and the distance Estrada ind...

Let l, k be fixed positive integers. In [1], the first and third authors established a bijection between l-cores with first part equal to k and (l − 1)-cores with first part less than or equal to k. This paper gives several new interpretations of that bijection. The l-cores index minimal length coset representatives for f Sl/Sl where f Sl denotes the affine symmetric group and Sl denotes the fi...

suppose $gamma$ is a graph with $v(gamma) = { 1,2, cdots, p}$and $ mathcal{f} = {gamma_1,cdots, gamma_p} $ is a family ofgraphs such that $n_j = |v(gamma_j)|$, $1 leq j leq p$. define$lambda = gamma[gamma_1,cdots, gamma_p]$ to be a graph withvertex set $ v(lambda)=bigcup_{j=1}^pv(gamma_j)$ and edge set$e(lambda)=big(bigcup_{j=1}^pe(gamma_j)big)cupbig(bigcup_{ijine(gamma)}{uv;uin v(gamma_i),vin ...

Let be a G-symmetric graph admitting a nontrivial G-invariant partition B. For B∈B, let D(B)= (B; B(B); I) be the 1-design in which IC for ∈B and C ∈ B(B) if and only if is adjacent to at least one vertex of C, where B(B) is the neighbourhood of B in the quotient graph B of relative to B. In a natural way the setwise stabilizer GB of B in G induces a group of automorphisms of D(B). In this pape...

‎In this paper‎, ‎exact formulas for the dependence‎, ‎independence‎, ‎vertex cover and clique polynomials of the power graph and its‎ ‎supergraphs for certain finite groups are presented‎.

We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph G has perfect state transfer if and only if its quotient G/π, under any equitable partition π, has perfect state transfer, we exhibit graphs with perfect state transfer between two vertices but which lack automorphism swapping them. This answers a question of Godsil (Discrete Mathematics 312(1):129...

The A* algorithm is defined in a directed graph formalism. Pruning, path merging and modzfication of the algorithm to output word graphs rather than N-best lists are discussed. The concept of quotient graphs is utilised to improve the lexical graph. Results j-om experiments with the continuous speech recognition task of the WAXHOLM project are reported. The use of a particular quotient graph in...

Throughout this paper, G denotes a simple and simply connected algebraic group over C of rank r and H is a Cartan subgroup, with Lie algebras g = LieG and h = LieH. Let R be the root system of the pair (G,H), W the Weyl group, and Λ ⊆ h the coroot lattice. Fix once and for all a positive Weyl chamber, i.e. a set of simple roots ∆. The geometric invariant theory quotient of g by the adjoint acti...

We establish a geometrical framework for the study of imprimitive, G-symmetric graphs F by exploiting the fact that any G-partition B of the vertex set VT gives rise both to a quotient graph fB and to a tactical configuration D(B) induced on each block B e B . We also examine those cases in which D(B) is degenerate, and characterize the possible graphs f in many cases where the quotient FB is e...

Let Γ be a G-symmetric graph, and let B be a nontrivial G-invariant partition of the vertex set of Γ . This paper aims to characterize (Γ ,G) under the conditions that the quotient graph ΓB is (G, 2)-arc transitive and the induced subgraph between two adjacent blocks is 2 · K2 or K2,2. The results answer two questions about the relationship between Γ and ΓB for this class of graphs. c © 2007 El...