In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...

Graph grammars have been studied by several authors. The motivations of these works have arisen from completely different areas of computer science, such as picture processing (Pfaltz and Rosenfeld, 1969; Montanari, 1970; Rosenfeld and Milgram, 1972; Pavlidis, 1972; Abe et al., 1973; Furtado and Mylopoulos, 1975; Fu and Brayer, 1975) or formal semantics of programming languages (Pratt, 1971). I...

graph theory based methods are powerful means for representing structural systems so that their geometry and topology can be understood clearly. the combination of graph theory based methods and some metaheuristics can offer effective solutions for complex engineering optimization problems. this paper presents a charged system search (css) algorithm for the free shape optimizations of thin-wall...

A metric graph is a pair (G, d), where G and $$d:E(G) \rightarrow \mathbb {R}_{\ge 0}$$ distance function. Let $$p \in [1,\infty ]$$ be fixed. An isometric embedding of the d) in $$\ell _p^k = (\mathbb {R}^k, d_p)$$ map $$\phi :V(G) {R}^k$$ such that $$d_p(\phi (v), \phi (w)) d(vw)$$ for all edges $$vw\in E(G)$$ . The _p$$ -dimension least integer k there exists an _p^k$$ functions d has _p^K$$...

Abstract We propose a novel graph-based approach for semantic parsing that resolves two problems observed in the literature: (1) seq2seq models fail on compositional generalization tasks; (2) previous work using phrase structure parsers cannot cover all parses treebanks. prove both MAP inference and latent tag anchoring (required weakly-supervised learning) are NP-hard problems. optimization al...