منابع مشابه
Hypomorphy of graphs up to complementation
Let V be a set of cardinality v (possibly infinite). Two graphsG and G with vertex set V are isomorphic up to complementation if G is isomorphic to G or to the complement G of G. Let k be a non-negative integer, G and G are k-hypomorphic up to complementation if for every k-element subsetK of V , the induced subgraphs G↾K and G′↾K are isomorphic up to complementation. A graph G is k-reconstruct...
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Considering uniform hypergraphs, we prove that for every non-negative integer h there exist two non-negative integers k and t with k ≤ t such that two h-uniform hypergraphs H and H′ on the same set V of vertices, with ∣V ∣ ≥ t, are equal up to complementation whenever H and H′ are k-hypomorphic up to complementation. Let s(h) be the least integer k such that the conclusion above holds and let v...
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In order to generalize the Kleene theorem from the free monoid to richer algebraic structures, we consider the non deterministic acceptance by a finite automaton of subsets of vertices of a graph. The subsets accepted in such a way are the equational subsets of vertices of the graph in the sense of Mezei and Wright. We introduce the notion of deterministic acceptance by finite automaton. A grap...
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We initiate the study of reducts of relational structures up to primitive positive interdefinability: After providing the tools for such a study, we apply these tools in order to obtain a classification of the reducts of the logic of equality. It turns out that there exists a continuum of such reducts. Equivalently, expressed in the language of universal algebra, we classify those locally close...
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Recently, Berman and Zhang (Discrete Math. 260 (2003) 27) obtained an upper bound for the bipartite density of cubic graphs in terms of the smallest eigenvalue of an adjacency matrix and attempted to characterize graphs for which the upper bound is attained. Here we do characterize graphs for which the upper bound is attained, and correct a few errors from Berman and Zhang’s paper. c © 2004 Els...
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ژورنال
عنوان ژورنال: Arabian Journal of Mathematics
سال: 2020
ISSN: 2193-5343,2193-5351
DOI: 10.1007/s40065-020-00297-8