International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 3, Pages 145-149

Characterizing symmetric diametrical graphs of order 12 and diameter 4

S. Al-Addasi1 and H. Al-Ezeh2

1Department of Mathematics, Hashemite University, Zarqa, Jordan
2Department of Mathematics, University of Jordan, Amman, Jordan

Received 21 March 2001; Revised 29 August 2001

Copyright © 2002 S. Al-Addasi and H. Al-Ezeh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A diametrical graph G is said to be symmetric if d(u,v)+d(v,u¯)=d(G) for all u,vV(G), where u¯ is the buddy of u. If moreover, G is bipartite, then it is called an S-graph. It would be shown that the Cartesian product K2×C6 is not only the unique S-graph of order 12 and diameter 4, but also the unique symmetric diametrical graph of order 12 and diameter 4.