Speaker : Prof. Seok-Zun Song (Jeju National University)
Date : 16:00-17:00, November 21, 2018
Place : AORC Seminar Room
Title : Genus of a graph and its linear preserving operators
Abstract:
A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k&pe_Qc;1. A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k + 1 to graphs of genus k + 1. We show that such linear operators are necessarily vertex permutations. Similar results with different restrictions on the genus k preserving operators give the same conclusion.