In this paper, we propose a new approach to inheritance in the context of algebraic graph transformation by providing a suitable categorial framework which reflects the semantics of class-based inheritance in software engineering. Inheritance is modelled by a type graph T that comes equipped with a partial order. Typed graphs are arrows with codomain T which preserve graph structures up to inhe...

Let G be an undirected graph with vertices {v1, v2, . . . , vν} and edges {e1, e2, . . . , eε}. Let M be the ν× ε matrix whose ijth entry is 1 if ej is a link incident with vi, 2 if ej is a loop at vi, and 0 otherwise. The matrix obtained by orienting the edges of a loopless graph G (i.e., changing one of the 1s to a −1 in each column of M) has been studied extensively in the literature. The pu...

The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, is a remarkable measure to unfold the robustness of complex networks. In this paper we study the asymptotic behavior of the algebraic connectivity in the Erdős-Rényi random graph, the simplest model to describe a complex network. We estimate analytically the mean and the variance of the algebraic c...

In this paper a tight lower bound for algebraic connectivity of graphs (second smallest eigenvalue of the Laplacian matrix of the graph) based on connection-graph-stability method is introduced. The connection-graph-stability score for each edge is defined as the sum of the length of all the shortest paths making use of that edge. We prove that the algebraic connectivity of the graph is lower b...

We perform the asymptotic enumeration of two classes of rooted maps on orientable surfaces:m-hypermaps andm-constellations. Form = 2 they correspond respectively to maps with even face degrees and bipartite maps. We obtain explicit asymptotic formulas for the number of such maps with any finite set of allowed face degrees. Our proofs combine a bijective approach, generating series techniques re...

Abstract In the ( G , H )-isomorphism game, a verifier interacts with two non-communicating players (called provers), by privately sending each of them random vertex from either or . The goal is to convince that graphs and are isomorphic. recent work along Atserias et al. (J Comb Theory Ser B 136:89–328, 2019) we showed can be convinced non-isomorphic isomorphic, if provers allowed share quantu...

Abstract The ability of molecular property prediction is great significance to drug discovery, human health, and environmental protection. Despite considerable efforts, quantitative various properties remains a challenge. Although some machine learning models, such as bidirectional encoder from transformer, can incorporate massive unlabeled data into representations via self-supervised strategy...