Multicore Graphs: Characterization and Properties

In this paper we define the multicore graphs, a subclass of chordal graphs that extends the gen core-satellite graphs, defined by Estrada and Benzi (Linear Algebra App. 517:30–52 (2017)) [5]. We prove that the multicore graphs are the \((P_5,gem,dart)\) -free chordal graphs and we present a characterization of the class which provides a simple linear time recognition algorithm. We also show its interrelation with other subclasses of chordal graphs: the clique-corona graphs and the starlike graphs.