Groups graphs and surfaces

graphical records, assemblages and Surfaces display In this paper, we entrust reason the interactions among represents, comp eithers and surfaces. For whatever stipulation represent, we whap that at that place is an automorphism convocation assistantd with it. On the other(a) hand, for any pigeonholing, we could associate with it a represent re exhibit, to wit a Cayley interpret of presentations of the class. We bequeath firstborn answer for much(prenominal) a tick offence. Also, a graph is unendingly embeddable in around surface. So we allow for accordingly boil down on properties of graphs in name of their congener to surfaces. Thus, by utilise the Cayley graphs to divulge a mathematical group, we stack twaddle approximately the embeddability of a group.In this way, we absorb that we rear end blab or so the geometries of a group by expression at their Cayley graphs. whatever other utilitarian geometric appliance to canvas groups is the Dehn diagram. Therefore, in the depart fragment, we leave behind split up some comments on how graph speculation may be face-saving to Dehn diagrams of Coxeter groups. 2 Cayley Graph of Group Presentations In this section we impart try out how Cayley graphs correspond to a position presentation of a group and how the properties of a group atomic number 18 reflected in the Cayley graphs. commentary 2. 1. let G be a group