Abstract Graph neural networks (GNN) have been shown to provide substantial performance improvements for atomistic material representation and modeling compared with descriptor-based machine learning models. While most existing GNN models predictions are based on atomic distance information, they do not explicitly incorporate bond angles, which critical distinguishing many structures. Furthermo...

A graph is representable if there exists a word over the alphabet such that letters  = , G V E  W V x and alternate in W if and only if y   , x y is in E for each x not equal to . The motivation to study representable graphs came from algebra, but this subject is interesting from graph theoretical, computer science, and combinatorics on words points of view. In this paper, we prove that for...

A signed graph is a graph in which every edge is designated to be either positive or negative; it is balanced if every cycle contains an even number of negative edges. A marked signed graph is a signed graph each vertex of which is designated to be positive or negative, and it is consistent if every cycle in the signed graph possesses an even number of negative vertices. Signed line graph L(S) ...

A graph G = (V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) is in E for each x not equal to y. The motivation to study representable graphs came from algebra, but this subject is interesting from graph theoretical, computer science, and combinatorics on words points of view. In this paper, we prove that for n gre...

This paper deals with the classification of groups G such that power graphs and proper are line graphs. In fact, we classify all finite nilpotent whose Also, categorize (except non-abelian 2-groups) Moreover, investigate when generalized quaternion Besides, derive a condition on order dihedral for which