Symmetry in Graph Theory

This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view

Complexity of diameter on AT-free graphs is linear

We develop a linear time algorithm for finding the diameter of an asteroidal triple-free (AT-free) graph. Furthermore, we update the definition of polar pairs and develop new properties of polar pairs for (weak) dominating pair graphs. We prove that the problem of computing a simplicial vertex in a general graph can be accomplished in O(n^2) based on an existing reduction to the problem of finding diameter in an AT-free graph. We improve the best-known run-time complexities of several graph theoretical problems

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum