• We adapt a traditional non-learnable GED algorithm to the novel paradigm of geometric deep learning. Triplet network for learning graph distances by means neural networks. Learning distance in domain without an embedding stage. Graph-based keyword spotting application with state-of-the-art performance. The emergence as framework deal graph-based representations has faded away approaches favor...

This paper introduces QuanTree v1.1 and QuanLin v1.1, two Java applications available for free. (Source code included in the distribution.) Each application compiles a different type of input quantum evolution operator. The applications output a quantum circuit that is approximately equal to the input evolution operator. QuanTree compiles an input evolution operator whose Hamiltonian is proport...

The characterization of distance-regular Cayley graphs originates from the problem identifying strongly regular graphs, or equivalently, partial difference sets. In this paper, a classification on dicyclic groups is obtained. More specifically, it shown that every graph group complete graph, multipartite non-antipodal bipartite with diameter 3 satisfying some additional conditions.

Let G and H be connected graphs. The tensor product G + H is a graph with vertex set V(G+H) = V (G) X V(H) and edge set E(G + H) ={(a , b)(x , y)| ax ∈ E(G) & by ∈ E(H)}. The graph H is called the strongly triangular if for every vertex u and v there exists a vertex w adjacent to both of them. In this article the tensor product of G + H under some distancebased topological indices are investiga...

In this paper we show that, for each chordal graph G, there is a tree T such that T is a spanning tree of the square G2 of G and, for every two vertices, the distance between them in T is not larger than the distance in G plus 2. Moreover, we prove that, if G is a strongly chordal graph or even a dually chordal graph, then there exists a spanning tree T of G that is an additive 3-spanner as wel...

let g = (v, e) be a simple graph. hosoya polynomial of g isd(u,v)h(g, x) = {u,v}v(g)x , where, d(u ,v) denotes the distance between vertices uand v. as is the case with other graph polynomials, such as chromatic, independence anddomination polynomial, it is natural to study the roots of hosoya polynomial of a graph. inthis paper we study the roots of hosoya polynomials of some specific graphs.

In this paper we show that, for each chordal graph G, there is a tree T such that T is a spanning tree of the square G2 of G and, for every two vertices, the distance between them in T is not larger than the distance in G plus 2. Moreover, we prove that, if G is a strongly chordal graph or even a dually chordal graph, then there exists a spanning tree T of G that is an additive 3-spanner as wel...

Let G be a simple connected graph. The transmission of any vertex v of a graph G is defined as the sum of distances of a vertex v from all other vertices in a graph G. Then the distance signless Laplacian matrix of G is defined as D^{Q}(G)=D(G)+Tr(G), where D(G) denotes the distance matrix of graphs and Tr(G) is the diagonal matrix of vertex transmissions of G. For a given minimum dominating se...

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...