Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

# Seminar of Graph Theory - Martin Knor (19.11.2020)

## Thursday 19.11.2020 at 9:50

17. 11. 2020 21.56 hod.

Martin Knor (Slovak University of Technology in Bratislava):
Distance based indices in nanotubical graphs

MS TEAMS code (users from Comenius University in Bratislava): gglxxc7
Link (guests outside Comenius University in Bratislava)

Abstract:
Nanotubical graphs are obtained by wrapping a hexagonal grid, and then possibly closing the tube with caps. We derive asymptotics for several distance-based generalized chemical indices which are of the form $$I^{\lambda}(G)=\sum_{u\ne v}f(u,v)dist^{\lambda}(u,v),$$ where $\lambda$ is a real number and $f(u,v)$ is a nonnegative symmetric function which is non-decreasing and which depends only on degrees of $u$ and $v$. All our results are obtained using double integrating and they show that the leading term depends on the circumference of the nanotube and not on its particular type.

This is a joint work with Vesna Andova and Riste Skrekovski