A direct vehicle-to-vehicle (V2V) charging scheme supplies flexible and fast energy exchange way for electric vehicles (EVs) without the supports of charging stations. Main technical challenges in cooperative V2V charging may include the efficient charging navigation structure designs with low communication loads and computational complexities, the decision-making intelligence for the selection of stopping locations to operate V2V charging services, and the optimal matching issue between charging EVs and discharging EVs. In this paper, to solve the above problems, we propose an intelligent V2V charging navigation strategy for a large number of mobile EVs. Specifically, by means of a hybrid vehicular ad-hoc networks (VANETs) based communication paradigm, we first study a mobile edge computing (MEC) based semi-centralized charging navigation framework to ensure the reliable communication and efficient charging coordination. Then, based on the derived charging models, we propose an effective local charging navigation scheme to adaptively select the optimal traveling route and appropriate stopping locations for mobile EVs via the designed Q-learning based algorithm. After that, an efficient global charging navigation mechanism is proposed to complete the best charging-discharging EV pair matching based on the constructed weighted bipartite graph. A series of simulation results and theoretical analyses are presented to demonstrate the feasibility and effectiveness of the proposed V2V charging navigation strategy. INDEX TERMSElectric vehicles, intelligent V2V charging, charging models, VANETs. NOMENCLATURE N mec Number of MEC servers. N sl Number of stopping locations. N v Number of all moving vehicles including EVs and oil-driven vehicles. PR ev Penetration ratio of EVs to all vehicles. PW Charging power of EVs. R Wireless communication range in VANETs. T Information broadcast interval of NCC. TA (SL k ) Arrival time of an EV in stopping location SL k . TC (SL k ) Charging time of an EV in stopping location SL k . TG (u, v) Arrival time gap between charging EV u and discharging EV v. TR (SL k ) Global traveling time of an EV moving from its current position to the destination going through stopping location SL k . N f (SL k ) Number of free slots in stopping location SL k in current time. T k (e i ) Average traveling time of a mobile EV going through road segment e i . T cw (SL k ) Charging waiting time of EVs for free slots in stopping location SL k . v k (e i ) Average traveling velocity of a mobile EV going through road segment e i . CC/CV Constant-current/constant-voltage. EV Eletric vehicle EVC EVs with charging requirements. EVD EVs with discharging abilities. EVN EVs without charging/discharging interests. G2V Grid-to-vehicle. IMC Information managing centers. ITS Intelligent transportation systems. KM Kuhn-Munkres-based algorithm. KWh KiloWatt-hour. LSTM Long short-term memory. MAC Media access control. MEC Mobile edge computing. MWM Maximum weighted matching. NCC Navigation control center. OBUs On board units...
As an extension of the Four-Color Theorem it is conjectured that every planar graph of odd-girth at least 2k + 1 admits a homomorphism to P C 2k = (Z 2k 2 , {e 1 , e 2 , · · · , e 2k , J}) where e i 's are standard basis and J is all 1 vector. Noting that P C 2k itself is of odd-girth 2k + 1, in this work we show that if the conjecture is true, then P C 2k is an optimal such a graph both with respect to number of vertices and number of edges. The result is obtained using the notion of walk-power of graphs and their clique numbers.An analogous result is proved for bipartite signed planar graphs of unbalanced-girth 2k. The work is presented on a uniform frame work of planar consistent signed graphs.
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