Slobodan Filipovski

collaborators

3 papers

math.CO2024

A partial proof of the Brouwer's conjecture

Slobodan Filipovski

Let $G$ be a simple graph with $n$ vertices and $m$ edges and let $k$ be a natural number such that $k \leq n .$ Brouwer conjectured that the sum of the $k$ largest Laplacian eigenva…

math.CO2024

Some results on $I ¨ _{t}$ -irregularity

Slobodan Filipovski, Darko Dimitrov, Martin Knor +1

The $I ¨ _{t}$ -irregularity (or sigma total index) is a graph invariant which is defined as $I ¨ _{t} (G) = \sum_{{u, v} \subseteq V (G)} (d (u) - d (v))^{2},$ where $d (z)$ denotes the degree o…

math.CO2024

Extremizing antiregular graphs by modifying total $I ¨ $ -irregularity

Martin Knor, Riste Å krekovski, Slobodan Filipovski +1

The total $I ¨ $ -irregularity is given by $I ¨ _{t} (G) = \sum_{{u, v} \subseteq V (G)} (d_{G} (u) - d_{G} (v))^{2},$ where $d_{G} (z)$ indicates the degree of a vertex $z$ within the g…

A partial proof of the Brouwer's conjecture

Some results on I¨t​-irregularity

Extremizing antiregular graphs by modifying total I¨-irregularity

Some results on $I ¨ _{t}$ -irregularity

Extremizing antiregular graphs by modifying total $I ¨ $ -irregularity