Guest Editorial: Special section on graph theory and its application in vehicular networking

T HE LAST TWO decades have witnessed unprecedented growth in telecommunications, particularly in the area of wireless communications. This development in telecommunications opens doors to many sophisticated complex systems, e.g., social networks, smart grids, vehicular networks, and sensor networks, which previously were not feasible. Graph theory is among the most widely used tools for modeling and analyzing the many types of interactions, relations, and dynamics in these systems. Many problems of practical interest can be represented by graphs. The use of graph theory in vehicular networks or, more broadly, highly dynamic networks is of particular interest. The complex interactions among vehicles, between vehicles and roadside infrastructure, combined with the high mobility of vehicles and fast changing network topology, present some unique challenges in network modeling and performance analysis, network design, resource management, communication protocol development, security protocol design, and localization. This Special Section aims at highlighting recent advances in graph theory that are applicable to highly dynamic networks, particularly vehicular networks, identifying challenges in the area and presenting possible solutions, and furthermore unveiling the significant potential of graph theory in the domain of vehicular networks. We received a total of 22 paper submissions , and all of them were of exceptionally high quality. Unfortunately, we are only able to accept eight papers for publication in this Special Section due to space limitations. The paper titled " Application of Graph Theory to the Multi-cell Beam Scheduling Problem " by Dartmann et al. applies com-binatorial optimization techniques to joint optimization of the beamforming vectors, power control, and beam scheduling along with multiuser scheduling to improve the downlink transmission in a multicell network where performance is limited by intercell interference. This joint optimization problem is called the beam scheduling problem in the paper, which is formulated as a graph-theoretic problem, more specifically, as a multidimensional assignment problem. The authors further propose four algorithms, each having different advantages, to solve the problem. The paper titled " Interference Graph-Based Resource-Sharing Schemes for Vehicular Networks " by Zhang et al. studies the resource sharing problem in vehicular ad hoc networks (VANETs) using an interference graph-based approach. Both vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) links are considered. They show that better sum rates can be achieved using the graph-based approach, which allows V2V and V2I links to coexist, compared with orthogonal communications. Further, the proposed algorithm is proven to have low complexity, and simulation results corroborate their findings. …