a lot of research and various techniques have been devoted for finding the topologicaldescriptor wiener index, but most of them deal with only particular cases. there exist threeregular plane tessellations, composed of the same kind of regular polygons namely triangular,square, and hexagonal. using edge congestion-sum problem, we devise a method to computethe wiener index and demonstrate this m...

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

Aldous and Fill conjectured that the maximum relaxation time for random walk on a connected regular graph with n $n$ vertices is ( 1 + o ) 3 2 ? $(1+o(1))\frac{3{n}^{2}}{2{\pi }^{2}}$ . This conjecture can be rephrased in terms of spectral gap as follows: (algebraic connectivity) k $k$ -regular at least $(1+o(1))\frac{2k{\pi }^{2}}{3{n}^{2}}$ , bound attained one value We determine structure qu...

Using a technique due to Jiménez–Rodríguez, first we prove the complete latticeability of set disjoint non-norm null weakly sequences and regular-polynomially in Banach lattices. Then apply mother vector ? ? ( E ) ? s $\lambda _\pi (E) \setminus \lambda _s(E)$ , which implies ? p ? ? | $(\ell _p\widehat{\otimes }_{|\pi |}E)\setminus (\ell }_{\pi }E)$ where is lattice 1 < ? $1 \infty$ .

On a regular tetrahedron in spherical space there exist the finite number of simple closed geodesics. For any pair coprime integers $(p,q)$ it was found numbers $\alpha_1$ and $\alpha_2$ depending on $p$, $q$ satisfying inequalities $\pi/3< \alpha_1 < \alpha_2 2\pi/3$ such that with faces angle $\alpha \in \left( \pi/3, \right)$ exists unique, up to rigid motion tetrahedron, geodesic type $(p,q...