4 research outputs found
Connectivity and diameter in distance graphs
For and , the distance graph has vertex set and edge set . The class of distance graphs generalizes the important and very well-studied class of circulant graphs which have been proposed for numerous network applications. In view of fault tolerance and delay issues in these applications, the connectivity and diameter of circulant graphs have been studied in great detail. Our main contributions are hardness results concerning computational problems related to the connectivity and diameter of distance graphs and a number-theoretic characterization of the connected distance graphs for
Diameter of generalized Petersen graphs
Due to their broad application to different fields of theory and practice,
generalized Petersen graphs have been extensively investigated.
Despite the regularity of generalized Petersen graphs, determining an exact
formula for the diameter is still a difficult problem. In their paper, Beenker
and Van Lint have proved that if the circulant graph has diameter
, then has diameter at least and at most . In this
paper, we provide necessary and sufficient conditions so that the diameter of
is equal to and sufficient conditions so that the diameter of
is equal to Afterwards, we give exact values for the diameter
of for almost all cases of and Furthermore, we show that
there exists an algorithm computing the diameter of generalized Petersen graphs
with running time (log)