Pentagon-Generated Trivalent Graphs with Girth 5
- 1 February 1971
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 23 (1) , 36-47
- https://doi.org/10.4153/cjm-1971-004-0
Abstract
The terminology of [1] will be assumed in what follows. LetPb(G) stand for the set of pentagons in the graphG.Call a graphpentagongeneratedwhen it is the union of its contained pentagons. LetP5,3be the class of connected trivalent pentagon-generated graphs with girth 5. These graphs form a family including the Petersen graph and the graph of the dodecahedron. They are studied here and completely classified in terms of a decomposition which all but some specifically determined indecomposable graphs admit.Assume henceforth thatH∈P5,3. LetEk(H) be the set of edges in exactlyk∈ 0 pentagons ofH. ClearlyEk(H) = 0 ifk≠ 1, 2, 3, 4 and |E1(H) ∩E(P)r ≦ 2, for allP∈P5(H).P∈P5(H) issingularwhen |E1(H) ∩E(P)r = 2,.Keywords
This publication has 1 reference indexed in Scilit:
- Connectivity in GraphsPublished by University of Toronto Press Inc. (UTPress) ,1966