TY - JOUR
AU - Thomson, Alison
AU - ZHOU, SANMING
Y2 - 2014/05/22
Y1 - 2008
UR - http://hdl.handle.net/11343/33003
AB - A first kind Frobenius graph is a Cayley graph Cay.K; S/ on the Frobenius kernel of a Frobenius group K o H such that S D aH for some a 2 K with haH i D K, where H is of even order or a is an involution. It is known that such graphs admit â€˜perfectâ€™ routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as models for interconnection networks, it is thus highly desirable to characterize those which are Frobenius of the first kind. In this paper we first give such a characterization for connected 4-valent circulant graphs, and then describe optimal routing and gossiping schemes for those which are first kind Frobenius graphs. Examples of such graphs include the 4-valent circulant graph with a given diameter and maximum possible order.
LA - eng
PB - Cambridge University Press
KW - Cayley graph
KW - circulant graph
KW - multi-loop network
KW - double-loop network
KW - Frobenius group
KW - Frobenius graph
KW - complete rotation
KW - gossiping
KW - minimum gossip time
KW - routing
KW - edgeforwarding
KW - index
KW - arc-forwarding index
T1 - Frobenius circulant graphs of valency four
DO - 10.1017/S1446788708000979
IS - Journal of the Australian Mathematical Society
VL - 85
IS - 2
SP - 269-282
L1 - /bitstream/handle/11343/33003/294792_FROBENIUS%20CIRCULANT.pdf?sequence=1&isAllowed=y
ER -