journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2258 Distance-balancing of cube-connected cycles graphs Aouina Mokhtar Department of Mathematics and Philosophy, Western Illinois University, Macomb, Illinois, 61455, U.S.A. Karami Hamed Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, 30303, U.S.A. LaFountain Douglas J. Department of Mathematics and Philosophy, Western Illinois University, Macomb, Illinois, 61455, U.S.A. 28 7 2849 2861 25 10 2025

We show that the cube-connected cycles graphs CCCn are distance-balanced via an investigation of the automorphisms of CCCn. We then introduce a new diagrammatic way to represent minimal paths in CCCn, termed interval-with-ends diagrams, and use this to prove that CCCn is nicely distance-balanced if and only if n is even. We also observe that CCCn fails to be distance-regular for all n. 

 Distance-balanced Nicely distance-balanced Cube-connected cycles graphs Automorphisms Interval-with-ends diagrams access open retracted no