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Atlantic Graph Theory Seminar

January 29, 2025 @ 3:30 pm - 4:30 pm

Switching m-edge coloured graphs
Speaker: Gary MacGillivray, University of Victoria
Abstract:

An m-edge-coloured graph consists of a set of vertices, any two of which are either joined by an edge of one of m colours or not joined at all. The operation of switching at a vertex v of an m-edge-coloured graph with respect to an element of a subgroup \Gamma of S_m  permutes the colours of the edges incident with v.  Switching defines an equivalence relation on the set of all m-edge-coloured graphs;  G and H are \Gamma-switch-equivalent if there exists a sequence of switches that transform G into H.

We consider the following problems and their solutions.  For a fixed subgroup \Gamma of S_m:
1) determine the number of equivalence classes of k-vertex m-edge-coloured graphs under switching with respect to \Gamma.
2) how hard is it to determine whether given m-edge-coloured graphs G and H are \Gamma-switch equivalent?
3) for a fixed m-edge-coloured graph H, how hard is it to determine whether a given m-edge-coloured graph G can be switched with respect to \Gamma so that there is a homomorphism of the transformed m-edge-coloured graph to H?  (A homomorphism is a mapping of V(G) to V(H) that preserves edges and colours.)

We will also discuss extending these results to (m,n)-mixed graphs.  These have m different colours of edges and n different colours of arcs.

 
Zoom link:
Meeting ID: 868 6149 9971
Passcode: 325258

Details

Date:
January 29, 2025
Time:
3:30 pm - 4:30 pm
Event Category:
Website:
https://us02web.zoom.us/j/86861499971?pwd=rTDAaju0TCu24asnaBGvkuNlT11KZ1.1

Venue

Online via Zoom

Organizer

jeannette Janssen
Phone:
(902) 494-8851
Email:
jeannette.janssen@dal.ca
Website:
https://www.dal.ca/faculty/science/math-stats/faculty-staff/our-faculty/mathematics/jeannette-janssen.html