Skip to main content
Figure 2 | Fixed Point Theory and Applications

Figure 2

From: A Brouwer fixed-point theorem for graph endomorphisms

Figure 2

A graph G of order 8 and size 9 with automorphism group S 2 Ă— S 2 . T 1 =Id with 8 fixed vertices of index 1 and 9 fixed edges of index −1 has Lefschetz number L(T)=−1. T 2 has 6 fixed vertices of index 1 and 5 fixed edges of index −1 with Lefschetz number L( T 2 )=1. T 3 has two fixed vertices of index 1 and one edge of index 1 leading to L( T 3 )=3. T 4 finally has only one fixed edge of index 1.

Back to article page