The Distance Energy of Wheel Graphs: A Comprehensive Analysis
Author : Dr. SB Kachale and Dr. RB Sahane
Abstract :
This research paper investigates the distance energy of various forms of wheel graphs including standard wheel graphs, wheel graphs with a cord, wheel graphs with removed spoke, bipartite wheel graphs, double wheel graphs and star graphs as a special case. The main result includes closed-form expressions for the distance energy of these graphs, specifically, we derive that the distance energy DE(Wn) of standard wheel graph Wn is 2(n - 1)√2 Additionally, we explore the effect of structural modifications on the distance energy, such as adding a cord, removing a spoke or considering bipartite and double wheel configurations. These findings contribute to a deeper understanding of the special properties of these graphs, with potential implications for further research in spectral graph theory.
Keywords :
Wheel graph, distance energy, spectral graph theory, bipartite graphs, double wheel graphs, star graphs
