On strictly Deza graphs with parameters (n,k,k-1,a)

A nonempty $k$-regular graph $\Gamma$ on $n$ vertices is called a Deza graph if there exist constants $b$ and $a$ $(b \geq a)$ such that any pair of distinct vertices of $\Gamma$ has precisely either $b$ or $a$ common neighbours. The quantities $n$, $k$, $b$, and $a$ are called the parameters of $\Gamma$ and are written as the quadruple $(n,k,b,a)$. If a Deza graph has diameter 2 and is not strongly regular, then it is called a strictly Deza graph. In the paper we investigate strictly Deza graphs with parameters $(n, k, b, a)$, where its quantities satisfy the conditions $k = b + 1$ and $\frac{k(k - 1) - a(n - 1)}{b - a} > 1$.Comment: Any comments or suggestions are very welcom

Plasmonic waveguides cladded by hyperbolic metamaterials

Strongly anisotropic media with hyperbolic dispersion can be used for claddings of plasmonic waveguides. In order to analyze the fundamental properties of such waveguides, we analytically study 1D waveguides arranged of a hyperbolic metamaterial (HMM) in a HMM-Insulator-HMM (HIH) structure. We show that hyperbolic metamaterial claddings give flexibility in designing the properties of HIH waveguides. Our comparative study on 1D plasmonic waveguides reveals that HIH-type waveguides can have a higher performance than MIM or IMI waveguides

Spectra of strongly Deza graphs

A Deza graph $G$ with parameters $(n,k,b,a)$ is a $k$-regular graph with $n$ vertices such that any two distinct vertices have $b$ or $a$ common neighbours. The children $G_A$ and $G_B$ of a Deza graph $G$ are defined on the vertex set of $G$ such that every two distinct vertices are adjacent in $G_A$ or $G_B$ if and only if they have $a$ or $b$ common neighbours, respectively. A strongly Deza graph is a Deza graph with strongly regular children. In this paper we give a spectral characterisation of strongly Deza graphs, show relationships between eigenvalues, and study strongly Deza graphs which are distance-regular