On the spectral characterization of Kite graphs

The \textit{Kite graph}, denoted by $Kite_{p,q}$ is obtained by appending a complete graph $K_{p}$ to a pendant vertex of a path $P_{q}$. In this paper, firstly we show that no two non-isomorphic kite graphs are cospectral w.r.t adjacency matrix. Let $G$ be a graph which is cospectral with $Kite_{p,q}$ and the clique number of $G$ is denoted by $w(G)$. Then, it is shown that $w(G)\geq p-2q+1$. Also, we prove that $Kite_{p,2}$ graphs are determined by their adjacency spectrum

On the spectral characterization of pineapple graphs

The pineapple graph $K_p^q$ is obtained by appending $q$ pendant edges to a vertex of a complete graph $K_{p}$ ($q\geq 1,\ p\geq 3$). Zhang and Zhang ["Some graphs determined by their spectra", Linear Algebra and its Applications, 431 (2009) 1443-1454] claim that the pineapple graphs are determined by their adjacency spectrum. We show that their claim is false by constructing graphs which are cospectral and non-isomorphic with $K_p^q$ for every $p\geq 4$ and various values of $q$. In addition we prove that the claim is true if $q=2$, and refer to the literature for $q=1$, $p=3$, and $(p,q)=(4,3)$

Bedesten:Bir kapalı kutu...

Taha Toros Arşivi, Dosya No: 8-Kapalıçarşıİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

A bound on the spectral radius of a weighted graph

Let G be simple, connected weighted graphs, where the edge weights are positive definite matrices. In this paper, we will give an upper bound on the spectral radius of the adjacency matrix for a graph G and characterize graphs for which the bound is attained

On the bounds for the largest Laplacian eigenvalues of weighted graphs

AbstractWe consider weighted graphs, such as graphs where the edge weights are positive definite matrices. The Laplacian eigenvalues of a graph are the eigenvalues of the Laplacian matrix of a graph G. We obtain an upper bound for the largest Laplacian eigenvalue and we compare this bound with previously known bounds

On the spectral characterization of mixed extensions of P₃

A mixed extension of a graph G is a graph H obtained from G by replacing each vertex of G by a clique or a coclique, whilst two vertices in H corresponding to distinct vertices x and y of G are adjacent whenever x and y are adjacent in G. If G is the path P3, then H has at most three adjacency eigenvalues unequal to 0 and -1. Recently, the first author classified the graphs with the mentioned eigenvalue property. Using this classification we investigate mixed extension of P3 on being determined by the adjacency spectrum. We present several cospectral families, and with the help of a computer we find all graphs on at most 25 vertices that are cospectral with a mixed extension of P_3

Sandal ağacı katkılı polipropilen kompozitlerin üretimi ve karakterizasyonu

xi, 40 sayfa29 cm. 1 CDÖZETOdun tozu katkılı termoplastik kompozitler bina cephe kaplamaları, yer döşemeleri, pencere ve kapı pervazları, çit, oturma bankı, peyzaj ürünleri ve otomotiv iç aksam parçaları gibi yapısal olmayan birçok uygulama alanına sahiptir. Bu tür ürünler ağaç ürünlerine alternatif olarak üretilmektedir. Odun tozu katkılı termoplastik kompozitler, ağacın dayanımına ve plastiklerin çevre koşullarına karşı dayanıklılığına sahiptirler. Bu tür kompozitler neme maruz olan uygulamalarda yaygın olarak kullanılmaktadır. Ancak, mevcut ticari odun tozlarına alternatif olarak yeni dolgu veya takviye malzemelerine ihtiyaç duyulmaktadır. Bu projede, öncelikle, sandal ağacından elde edilen partiküllerin partikül boyutları tespit edilecek ve kristalografik yapıları, ısıl dayanımları, yüzey fonksiyonel grupları, ve morfolojik özellikleri incelenecektir. Daha sonra elde edilen partiküller kullanılarak, sandal ağacı dolgulu polipropilen kompozitler üretilecektir. Kompozit üretiminde, polipropilen içerisine katılan dolgu miktarı değiştirilecektir. Üretilen kompozitlerin mekanik özellikleri (çekme dayanımı ve modülü, eğilme dayanımı ve modülü) üniversal test cihazı ile, ısıl özellikleri termogravimetrik analiz ve diferansiyel taramalı kalorimetre cihazları ile(TGA ve DSC), viskoelastik özellikleri dinamik mekanik analizi (DMA) ile ve morfolojik özellikleri taramalı elektron mikroskobu (SEM) ile incelenmiştir.ABSTRACTWood flour filled thermoplastic composites have used many non-structural applications such as side- coating, floor coverings, window and door trim, fence, sitting bench, landscaping products and automotive interior parts. Such products are produced as an alternative to wood products. Wood flour filled thermoplastic composites have the strength of wood and the resistance to environmental conditions of plastics. Such composites are widely used in wet applications. However, new fillers or reinforcing materials are needed as an alternative to existing commercial wood powders. In this project, firstly, the particle sizes of the particles obtained from sandalwood will be determined and the crystallographic structures, thermal properties, surface functional groups, and morphological characteristics examined. Subsequently, sandalwood filled polypropylene composites were produced by using the particles. In composite production, the amount of filler added to the polypropylene was changed. The mechanical properties (tensile strength and modulus, flexural strength and modulus), thermal,viscoelastic and morphological properties of the composites were evaluated by universal test machine, Thermogravimetric analysis and differential scanning calorimetry (with TGA and DSC), dynamic mechanical analysis (DMA) and scanning electron microscopy (SEM) instruments, respectively