We consider the number of spanning trees in circulant graphs of βn vertices with generators depending linearly on n. The matrix tree theorem gives a closed formula of βn factors; while we derive a formula of β−1 factors. The spanning tree entropy of these graphs is then compared to the one of fixed generated circulant graphs.

We give an explicit construction of circulant graphs of very high energy. This construction is based on Gauss sums. We also show the Littlewood conjecture can be used to establish new result for a certain class of circulant graphs. © 2005 Elsevier Inc. All rights reserved. AMS classification: 05C35; 05C50; 11T24; 42A05

‎Bucket recursive trees are an interesting and natural‎ ‎generalization of ordinary recursive trees and have a connection‎ to mathematical chemistry‎. ‎In this paper‎, ‎we give the lower and upper bounds for the moment generating‎ ‎function and moments of the multiplicative Zagreb indices in a‎ ‎randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$‎. Also, ‎we consi...

We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we construct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer ”YES”, by constructing a circulant weighing matrix of orde...

in this paper, we propose to extend the hierarchical bivariatehermite interpolant to the spherical case. let $t$ be an arbitraryspherical triangle of the unit sphere $s$ and  let $u$ be a functiondefined over the triangle $t$. for $kin mathbb{n}$, we consider ahermite spherical interpolant problem $h_k$ defined by some datascheme $mathcal{d}_k(u)$ and which admits a unique solution $p_k$in the ...

In this paper, we consider a g-circulant matrixA 1(T), whose the first row entries are generalized Tribonacci numbers T(a)i. We give an explicit formula of spectral norm matrix. When g = 1, also present upper and lower bounds for spread 1-circulant matrix A1(T).

We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations AX+XB=C, where the coefficient matrices A B are Toeplitz matrices. theoretical study shows that if factors of positive semi-definite (not necessarily Hermitian), at least one factor is definite, then CSCS converges to unique solution equation. In addition, our anal...