We consider the set G n,k of graphs of order n with the chromatic number k ≥ 2. In this note, we prove that in G n,k the Turán graph T n,k has the maximal spectral radius; and P n if k = 2, C n if k = 3 and n is odd, C 1 n−1 if k = 3 and n is even, K (l) k if k ≥ 4 has the minimal spectral radius. Thus we answer a problem raised by Cao [D.
Let ζ(s 1 , s 2 , · · · , s k ; α) be the multiple Hurwitz zeta function. Given two positive integers k and n with k n, let E(2n, k; α) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. In this note we present some generating series for the numbers E(2n, k; α).
The wheat stripe rust resistance gene Yr36 ( WKS1 ) with a unique kinase-START domain architecture is highly conserved in wild emmer wheat natural populations. Wild emmer wheat (Triticum dicoccoides) populations have developed various resistance strategies against the stripe rust pathogen Puccinia striiformis f. sp. tritici (Pst). The wild emmer gene, Yr36… (More)