# Seminar za računarstvo i primenjenu matematiku, 24. maj 2022.

Naredni sastanak Seminara biće održan u utorak, 24. maja 2022, u sali 301f sa početkom u 14.15 časova. Sastanak seminara je moguće pratiti i na daljinu.

Predavač: Mirko Lepović

Naslov predavanja: 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 ONTEGRAL GRAPHS

Apstrakt: 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 $(i)$ $a,p,q\in\mathbb N$ so that $2a\le p-1$, $2a-2\le q-1$ and $(p,q) = 1$; $(ii)$ $(x_0,y_0)$ is a particular solution of the linear Diophantine equation $px - qy = 1$ and $(iii)$ $z\ge z_0$ where $z_0$ is the least integer such that $\big(x_0 + qz_0\big)\ge 1$ and $\big(y_0 + pz_0\big)\ge 1$.

Napomena: Sastanak Seminara se može pratiti na daljinu preko linka
https://miteam.mi.sanu.ac.rs/asset/YoqHWKALRkRTbK9So

Za aktivno učešće neophodna je registracija preko linka:
https://miteam.mi.sanu.ac.rs/asset/xzGqvSp7aWbg8WpYX

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