A Graph Theoretical Approach for Frequency Reuse in a Mobile Computing Environment

Abstract

Effective ausage aof afrequency aresource ain aa amobile computing environment ais aa achallenging aproblem.The akey aidea ais ato acontrol amutual ainterference aamong aneighboring acells ain aa asystematic away aand aat athe asame atime aminimizing athe ausage aof afrequency autilization. aIn athis apaper awe apresent aa agraph atheoretic aapproach ato aaddress athis aproblem. aThe amutually ainterfering acells aare arepresented aas athe avertices aof aa agraph aand aa amathematical aassignment aof afrequencies ais adone ain aorder ato aavoid ainterference aup ato afour alevels asimultaneously afocusing aon athe aminimal ausage aof afrequency aresources. aThen athe aminimum avalue aof athe amaximum aassigned afrequency aamong aall asuch aassignments, acalled athe aspan aof athe agraph ais aobtained, awhich aserves aas athe ahighest afrequency ato abe aused ain aorder ato aavoid ainterference aup ato afour alevels. aIn athis apaper, awe adefine aa alabeling afor aany aconnected agraph awith aat aleast atwo avertices ahaving aa aHamiltonian apath aand amathematically aobtain athe aspan, aso aas aavoid ainterference aat afour alevels.