AUTOMATED CONJECTURING ON THE INDEPENDENCE NUMBER AND MINIMUM DEGREE OF DIAMETER-2-CRITICAL GRAPHS

A diameter-2-critical (D2C) graph is a graph with diameter two such that removing any edge increases the diameter or disconnects the graph. In this paper, we look at other lesser-studied properties of D2C graphs, focusing mainly on their independence number and minimum degree. We show that there exist D2C graphs with minimum degree strictly larger than their independence number, and that this gap can be arbitrarily large. We also exhibit D2C graphs with maximum number of common neighbors strictly greater than their independence number, and that this gap can be arbitrarily large. Furthermore, we exhibit a D2C graph whose number of distinct degrees in its degree sequence is strictly greater than its independence number. Additionally, we characterize D2C graphs with independence number 2 and show that all such graphs have independence number greater or equal to their minimum degree

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum