A maximal planar graph is a simple graph G formed by n vertices, 3(n−2) edges and 2(n−2) faces of degree 3 (all faces having degree 3). In this paper, our contribution is to propose the formula that ennumerate the number of spanning trees in the Lantern maximal planar graph L n to be τ (L n) = n−2 2 (2 + √ 3) n−2 + (2 − √ 3) n−2 − 2 , then we deduce formulas for its corresponding bipartite and reduced graphs.
Radio Frequency Identification (RFID) is considered as one of the most widely used wireless identification technologies in the Internet of Things. Many application areas require a dense RFID network for efficient deployment and coverage, which causes interference between RFID tags and readers, and reduces the performance of the RFID system. Therefore, communication resource management is required to avoid such problems. In this paper, we propose an anti-collision protocol based on feed-forward Artificial Neural Network methodology for distributed learning between RFID readers to predict collisions and ensure efficient resource allocation (DMLAR) by considering the mobility of tags and readers. The evaluation of our anti-collision protocol is performed for different mobility scenarios in healthcare where the collected data are critical and must respect the terms of throughput, delay, overload, integrity and energy. The dataset created and distributed by the readers allows an efficient learning process and, therefore, a high collision detection to increase throughput and minimize data loss. In the application phase, the readers do not need to exchange control packets with each other to control the resource allocation, which avoids network overload and communication delay. Simulation results show the robustness and effectiveness of the anti-collision protocol by the number of readers and resources used. The model used allows a large number of readers to use the most suitable frequency and time resources for simultaneous and successful tag interrogation.
In this paper, we consider the outerplanar graph L n [1], having 6n+6 vertices, 12n+9 edges and 6n+5 faces, in this graph all faces have degree 3 except for the outside face. Our approach consists on finding a general formula that calculates the number of spanning trees in the Ligth graph L n , depending on n.
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