Several matrices can be associated to a graph such as the adjacency matrix or the Laplacian matrix. The spectrum of these matrices gives some informations about the structure of the graph and the question “Which graphs are determined by their spectrum?” remains a difficult problem in algebraic graph theory. In this article we enlarge the known families of graphs determined by their spectrum by ...

In this study, by recognizing geographical location changes of the sun-path diagram, we present a selection of sustainable architectural guidelines that influence the climatic element of sunshine. For this purpose, after the introduction of triple zones of the earth in terms of how the sun is exposed(include:Tropical, temperate and polar), the function of the earth's curvature to create geograp...

let g be a (p, q) graph. let k be an integer with 2 ≤ k ≤ p and f from v (g) to the set {1, 2, . . . , k} be a map. for each edge uv, assign the label |f(u) − f(v)|. the function f is called a k-difference cordial labeling of g if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

The International Workshop on Molecular Mechanisms Controlling Flower Development took place in the secluded southern Italian village of Maratea in June 2011. This meeting, which takes place biennially, gathers researchers in the fields of flowering time and flower and fruit development from both Europe and overseas to enjoy the sun, the sea and, most importantly, the science. As we summarise h...

For n ∈ N and 3 ≤ k ≤ n we compute the exact value of Ek(n), the maximum number of edges of a simple planar graph on n vertices where each vertex bounds an l-gon where l ≥ k. The lower bound of Ek(n) is obtained by explicit construction, and the matching upper bound is obtained by using Integer Programming (IP.) We then use this result to conjecture the maximum number of edges of a non-flowerab...

Flower-like ZnO nanostructures were synthesized by a facile wet chemical method. Structural, optical and photocatalytic properties of these nanostructures have been studied by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), photoluminescence (PL) and UV-vis absorption spectroscopy. SEM and TEM studies revealed flower-like structures consistin...