Topic
Valency
About: Valency is a research topic. Over the lifetime, 1632 publications have been published within this topic receiving 26141 citations.
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TL;DR: This article put forward a valency theory of semantic underspefication, explicate its syntactic behavior, and demonstrate the valency of nominal modification, and propose an integrated description of the Valency theory along both the formal and semantic dimensions.
Abstract: With a purely structural perspective, either Valent Grammar or the valenty theory of the west is quite unable to give a comprehensive and natural account of the underlying semantic valency. We believe that an integrated description of the Valency theory must be adequate along both the formal and semantic dimensions, and that it must be adequate in its study of the predicate-argument structure, semantic underspecification, and situational elements. Therefore, we put forward a valency theory of semantic underspefication, explicate its syntactic behavior, and demonstrate the valency of nominal modification.
2 citations
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TL;DR: In this article, a complete classification of edge-transitive Cayley graphs of square-free order with valency less than the smallest prime divisor of the order has been given.
Abstract: Edge-transitive graphs of order a prime or a product of two distinct primes with any positive integer valency, and of square-free order with valency at most 7 have been classified by a series of papers. In this paper, a complete classification is given of edge-transitive Cayley graphs of square-free order with valency less than the smallest prime divisor of the order. This leads to new constructions of infinite families of both arc-regular Cayley graphs and edge-regular Cayley graphs (so half-transitive). Also, as by-products, it is proved that, for any given positive integers $$k,s\ge 1$$
and $$m,n\ge 2$$
, there are infinitely many arc-regular normal circulants of valency 2k and order a product of s primes, and there are infinitely many edge-regular normal metacirculants of valency 2m and order a product of n primes; such arc-regular and edge-regular examples are also specifically constructed.
2 citations
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2 citations