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The vertex-colouring problem is a well-known classical problem in graph theory in which a colour is assigned to each vertex of the graph such that no two adjacent vertices have the same colour. The minimum vertex-colouring problem is known as NP-hard problem in an arbitrary graph. In this paper a graph colouring algorithm based on modified incidence matrix is proposed for resolving Physical Cell ID (PCI) allocation for largescale femtocell deployment in LTE Telecommunication Networks. The proposed algorithm is not specified for neighbours only, but additionally can deal with neighbours of neighbours’ objects due to telecommunication requirements. Our results show that by applying proper searching and assigning methods it is possible to achieve satisfactory results for resource allocation in large and complex networks such as resolving PCI allocation and conflict for large femtocells deployment in LTE Networks., identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/13480

Femtocell or Home eNode cell in LTE is a home base station that anticipated to be deployed in very large numbers with fully automated manner. Femtocell provides enhanced coverage for in‐building cellular services. The enhanced data rates enable new multimedia services which in turn generate new revenue. However, with all the convenience such device can provide, locating the user’s geographic location represents a great deal of challenge for law enforcement and operators alike. In this work we propose a simple and direct approach that does not require any changes in the network or in the femtocell standard design by exploiting the connection between the femtocell and the network operator through the DSL backhaul. Result shows the proposed approach has achieved successfully the goal of locating the geographic location of the femtocell user precisely., identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/13475