By h(G, x) and P (G, λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fourth character R4(G), is given in this paper. Using the properties of the adjoint polynomials, the adjoint equivalence class of graph Bn−6,1,2 is determined, which can be regarded as the continuance of the paper written by Wang et al. [J. Wan...

We construct a universal cycle of n-permutations using n + 1 symbols and an equivalence relation based on differences. Moreover a complete family of universal cycles of this kind is constructed.

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We discuss and show correct an algorithm that constructs autostereograms. The concern is to develop a correct algorithm that may be implemented in a language such as C or Pascal.

For a class K of countable relational structures, a countable Borel equivalence relation E is said to be K-structurable if there is a Borel way to put a structure in K on each E-equivalence class. We study in this paper the global structure of the classes of K-structurable equivalence relations for various K. We show that K-structurability interacts well with several kinds of Borel homomorphism...