On Oriented Labelling Parameters
نویسندگان
چکیده
We introduce two notions, (i)oriented labelling and (ii) oriented labelling, to explore frequency assignment problem under halfduplex setting and compute bounds of oriented labelling of special classes of graphs : trees, bipartite graphs and planar graphs. We do study an oriented version of clique cover problem as well. The frequency assignment problem (FAP) arises in wireless communication systems. There are several models based on genetic algorithms, neural networks, constrained programming and combinatorial enumeration to explore and optimize different features of FAP such as available frequencies and limiting interference among radio signals. In 1970, Metzger [12] introduced graph coloring techniques as a tool to optimize the frequency spectrum used in FAP. Motivated by FAP, Hale [9] developed the concept of -coloring and it lead to many indepth graph theoretical results. A common feature of all these graph theoretical models of FAP is that they assume communication is viable in both direction (duplex) between two radio trasmitters and hence model FAP as a nonoriented graph. This is far away from reality. In fact, Aardal et al emphasised the importance of “direction/orientation” of transmission in their recent survey (for details see [1] page 4) on FAP. In this paper, we explore FAP under half-duplex setting (i.e., there are radio transimitters in a network in which at most one way transimission is effective between any two of them). Hence FAP can be modeled as an oriented multi graph. As a preliminary step, we focus on oriented simple graphs.
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تاریخ انتشار 2007