Tag Archives: Graph Theory

The cage problem and generalized polygons (part 1)

This post is a continuation of my previous post on the cage problem. Just to recall the main problem, for any given integers and , we want to find the least number of vertices in a simple undirected graph which … Continue reading

Posted in Combinatorics, Finite Geometry, Incidence Geometry, Spectral Graph Theory, Uncategorized | Tagged , , , , | Leave a comment

The Cage Problem

I recently finished my research visit to UWA where I worked with John Bamberg and Gordon Royle on some finite geometrical problems related to cages. So this seems like the right time for me to write a blog post about … Continue reading

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Expander Mixing Lemma in Finite Geometry

In this post I will discuss some nice applications of the expander mixing lemma in finite incidence geometry, including a new result that I have obtained recently. In many of the applications of the lemma in finite geometry, the graph is bipartite, and … Continue reading

Posted in Combinatorics, Finite Geometry, Incidence Geometry, Spectral Graph Theory | Tagged , , , , | 2 Comments

A note on the Hall-Janko near octagon

I recently found out via some computations in my research work that the Hall-Janko near octagon contains suboctagons isomorphic to the generalized octagon of order . I couldn’t find it mentioned anywhere in the literature but it seemed like something … Continue reading

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Strongly regular graphs

A graph is called regular if its every vertex has the same number of neighbours. For example, this is a regular graph where each vertex has exactly three neighbours: It is the well known Petersen graph which is so important and popular in graph … Continue reading

Posted in Combinatorics | Tagged | 3 Comments