Семинар за рачунарство и примењену математику, 3. март 2020.

Наредни састанак Семинара биће одржан у уторак, 3. марта 2020. у сали 301ф Математичког института САНУ са почетком у 14:15.

Предавач: Мирко Леповић, Природно-математички факултет, Универзитет у Крагујевцу

Наслов предавања: CONSTRUCTION TWO INFINITE CLASSES OF STRONGLY REGULAR GRAPHS USING MAGIC SQUARES

Апстракт: We say that a regular graph G of order n and degree r >= 1 (which is not the complete graph) is strongly regular if there exist non-negative integers $\tau$ and $\theta$ such that $|S_i\cap S_j| = \tau$ for any two adjacent vertices i and j and $|S_i\cap S_j|= \theta$ for any two distinct non-adjacent vertices i and j, where S_k denotes the neighborhood of the vertex k. Using a method for constructing the magic squares of order 2k+1 we have created two infinite classes of strongly regular graphs (i) strongly regular graph of order n = (2k+1)^2 and degree r = 8k with $\tau = 2k+5$ and $\theta = 12$ and (ii) strongly regular graph of order n = (2k+1)^2 and degree r = 6k with $\tau = 2k+1$ and $\theta = 6$ for k >= 2.