International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 3, Pages 145-149
doi:10.1155/S0161171202012474

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.

Abstract

A diametrical graph G is said to be symmetric if d(u,v)+d(v,u¯)=d(G) for all u,v∈V(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.