Наредни састанак Семинара биће одржан у уторак, 24. маја 2022, у сали 301ф са почетком у 14.15 часова. Састанак семинара је могуће пратити и на даљину.
Предавач: Мирко Леповић
Наслов предавања: ON INTEGRAL GRAPHS WHICH BELONG TO THE CLASS $\overline {\alpha G_a\cup \beta G_b}$ WHERE $G_a$ AND $G_b$ ARE TWO REGULAR INTEGRAL GRAPHS
Апстракт: Let G be a simple graph and let $\overline G$ denotes its complement. We say that G is integral if its spectrum consists entirely of integers. Let $G_a$ and $G_b$ be two regular integral graphs of order p and q and degree a and b, respectively. In this work we establish a characterization of integral graphs which belong to the class $\overline {\alpha G_a \cup\beta G_b}$, where mG denotes the m-fold union of the graph G. In particular,
(i) we demonstrate that there exists no integral graph from the class $\overline {\alpha G_a \cup\beta G_{a-1}}$ for $\alpha, \beta,a,p,q\in \mathbb N$ and
(ii) we demonstrate that if\enspace $\overline {\alpha G_a \cup \beta G_b}$ is integral with b=a-2 then it belongs to the class of integral graphs $\overline{\big(x_0 + qz\big)G_{2a} \cup\big(y_0 + pz\big)G_{2a-2}}$, where
- $a,p,q\in\mathbb N$ so that 2a <= p-1, 2a-2 <= q-1 and (p,q)=1;
- $(x_0,y_0)$ is a particular solution of the linear Diophantine equation px – qy = 1 and
- $z\ge z_0$ where $z_0$ is the least integer such that $\big(x_0 + qz_0\big)\ge 1$ and $\big(y_0 + pz_0\big)\ge 1$.
Напомена: Састанак Семинара се може пратити на даљину преко линка:
https://miteam.mi.sanu.ac.rs/asset/YoqHWKALRkRTbK9So
За активно учешће неопходна је регистрација преко линка:
https://miteam.mi.sanu.ac.rs/asset/xzGqvSp7aWbg8WpYX