The star graph, though an attractive alternative to the hypercube, has a major drawback in that the number of nodes for an n-star graph must be n!, and thus considerably limits the choice of the number of nodes in the graph. In order to alleviate this drawback, the arrangement graph was recently proposed as a generalization of the star graph topology. The arrangement graph provides more flexibility than the star graph in choosing the number of nodes, but the degree of the resulting network may be very high. To overcome that disadvantage, this paper presents another generalization of the star graph, called the (n,fc)-star graph. We examine some topological properties of the (n, fc)-star graph from the graph-theory point of view. It is shown that two different types of edges in the (n,fc)-star graph prevent it from being edge-symmetric, but edges in each class are essentially symmetric with respect to each other. Also, the diameter and the exact average distance of the (n, fc)-star graph are derived. In addition, the fault-diameter for the (n,fc)-star graph is shown to be at most the fault-free diameter plus three.

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SUMMARYThe services of next generation networks are envisioned to be potentially capable of seamless mobility in spite of the heterogeneity in underlying access technologies. It is undoubted that to accomplish seamless services across heterogeneous networking environments gets harder in case of simultaneous mobility. In this article, we propose a mobile-initiated network-executed (MINE) session initial protocol (SIP)-based handover mechanism to facilitate simultaneous mobility in IP multimedia subsystem over heterogeneous accesses. The novelty of the proposed approach is that no changes are required to the existing network infrastructure since handover decision is fully made by the mobile host (MH) and handover execution is performed by a new-added application server called mobility server (MS). When the MH decides to initiate a handover and obtains a new IP address, it will send a SIP Publish message to trigger the MS to carry out the handover execution. With the network-executed design of the MINE, the MS can perform third-party registration for security re-association and third-party call control for session re-establishment in parallel. Moreover, the Master-Slave Determination procedures derived from H.245 are used in the MS to handle fairly the racing conditions resulting from simultaneous mobility such that redundant message flows are eliminated. Mathematical analyses present that the MINE can shorten the handover latency and reduce power consumption, as observed from a comparison with the integrated solution of an optimized macro-mobility mechanism and a receiver-side simultaneous mobility approach.

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