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
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.