## Large vertex-transitive graphs and digraphs of given maximum degree and diameter

In this talk we present results devoted to the degree-diameter problem. The degree diameter problem means determination and searching for the largest graphs of given maximum degree and diameter. We discuss non - oriented as well as oriented version of this problem for vertex-transitive and Cayley version of this problem.

## The finite element A-Phi mehtod with composite grids for time-dependent eddy current problems

This talk is to investigate the finite element A-φ method with global coarse grids and local fine grids (composite grids) for solving a time-dependent eddy current problem, which can improve the accuracy of the coarse grid solutions in some subdomains of interest under properly increasing computational costs. Meanwhile, in order to decrease calculation complexity and avoid dealing with a saddle-point problem from the traditional A-φ scheme, we design an iteration which combines the composite grid method with the classic steepest descent such that the unknowns A and φ in the global coarse grids domain are decoupled and solved in two separate equations. We prove it converges with a bounded rate independent of two mesh sizes.

## Distributed order fractional diffusion-wave equations with time delay on bounded domains: a numerical approach

Distributed order fractional diffusion equations are used recently in describing physical phenomena such as modeling of waves in a viscoelastic rod of finite length and to describe radial groundwater flow to or from a well.
Time delay occurs frequently in realistic world and it has been considered in numerous mathematical models, e.g., automatic control systems with feedback, population dynamics. In the simulation of dynamical systems, two effects (distribution of parameters in space and delay in time) are often existed. We consider a numerical scheme for a class of non-linear time delay fractional diffusion equation with distributed order in time.
This study covers the unique solvability, convergence and stability of the resulted numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme is the main purpose of this study.