Raziskovalni matematični seminar - Arhiv
Let Γ be a connected G-arc-transitive graph, let uv be an arc of Γ and let L be the permutation group induced by the action of the vertex-stabiliser Gv on the neighbourhood Γ(v).
I will talk about the problem of bounding |Guv| in terms of L and the order of Γ.
On Monday, October 22, 2012, at the Faculty of Mathematics, Natural Sciences and Information Technologies in Koper, there will be a research mathematical seminar. Seminar starts at 10:00, and it will be organized in the "Seminar room" at Galeb (Kettejeva 1, Koper).
This Monday, we will have two lectures, both will last for approximately 25 minutes.
Abstract: Fullerene graphs are 3-connected planar cubic graphs with all
faces of size 5 or 6.
In the talk I will present a results regarding the diameter of
icosahedral fullerenes and fullerene graphs in general.
Abstract: Centrality is used to quantify an intuitive feeling that in
most networks some vertices are more central than others.
In the talk we consider some graph theoretical results on closeness,
betweenness centrality, and eccentricity.
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic.
We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-complementary graphs, give a characterization of natural numbers n for which there exists a square-complementary graph of order n, and characterize square-complementary graphs within various graph classes. The bipartite case turns out to be of particular interest.
Joint work with Anders Sune Pedersen, Daniel Pellicer and Gabriel Verret.