A bipartite graph G = ( V , E ) with 1 ∪ 2 is biregular if all the vertices of a stable set i have same degree r for . In this paper, we give an improved new Moore bound infinite family such graphs odd diameter. This problem was introduced in 1983 by Yebra, Fiol, and Fàbrega. Besides, propose some constructions diameter d large number N ; together their spectra. cases diameters 3 4, 5, attainin...

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In this article I consider the convergence of the Eilenberg– Moore spectral sequence for Morava K-theory. This spectral sequence can be constructed by applying Morava K-theory to D. L. Rector’s geometric cobar construction of the Eilenberg–Moore spectral sequence. I have shown that the Eilenberg–Moore spectral sequence for Morava Ktheory converges if the Eilenberg–Moore spectral sequence for or...

The nonexistence of digraphs with order equal to the Moore bound Md;k = 1+d+: : :+d k for d; k > 1 has lead to the study of the problem of the existence ofàlmost' Moore digraphs, namely digraphs with order close to the Moore bound. In 1], it was shown that almost Moore digraphs of order Md;k ? 1, degree d, diameter k (d; k 3) contain either no cycle of length k or exactly one such cycle. In thi...