On the Total Positivity of Delannoy-Like Triangles

On Tensor Product of Graphs, Girth and Triangles

The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.

A note on the bounds of Laplacian-energy-like-invariant

The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the num...

Similar Triangles, Another Trace of the Golden Ratio

In this paper we investigate similar triangles which are not congruent but have two pair congruent sides. We show that greatest lower bound of values for similarity ratio of such triangles is golden ratio. For right triangles, we prove that the supremum of values for similarity ratio is the square root of the golden ratio.

The Ill-Balanced Triangles of the Islamic States in Crisis

$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles

‎In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle‎. ‎We prove optimal estimates for the mapping properties of the Bergman projection on these domains.