Root graph

In graph theory , a root graph or root graph is a graph in which a node (the root ) has been distinguished. ${\displaystyle (G,o)}$ ${\displaystyle G}$ ${\displaystyle o}$

Graph with nodes ${\displaystyle G}$ ${\displaystyle a,b,c,d,e,f,g}$

Two root graph and are isomorphic if there is an isomorphism is that on maps. ${\displaystyle (G_{1},o_{1})}$ ${\displaystyle (G_{2},o_{2})}$ ${\displaystyle G_{1}\to G_{2}}$ ${\displaystyle o_{1}}$ ${\displaystyle o_{2}}$

Example: In the picture on the right, the root graphs are isomorphic to each other, but not to the other root graphs. and are also isomorphic to each other. is not isomorphic to any of the other root graphs. ${\displaystyle (G,b),(G,c),(G,d),(G,e)}$ ${\displaystyle (G,a)}$ ${\displaystyle (G,f)}$ ${\displaystyle (G,g)}$

Individual proof

1. ↑ Peter Tittmann: Introduction to combinatorics . 2014, ISBN 978-3-642-54588-7 , pp. 210 , doi : 10.1007 / 978-3-642-54589-4 ( springer.com [accessed May 10, 2018]).