Fold thickness of non-traceable cubic bridge graph / Cielo E. Nepomuceno, Crystal Jean T. Putian, and Mark Errol T. Red.

Undergraduate Thesis (BSAM)- Applied Mathematics. Camarines Sur Polytechnic Colleges, 2026.

Includes bibliographical references.

This study investigates the fold thickness of specific classes of Non-Traceable Cubic Bridge Graphs (NTCBGs), a family previously unexplored in this context. A 1-fold of a graph G is defined by identifying two nonadjacent vertices with a common neighbor and simplifying multiple edges. A uniform k-folding is a sequence of such operations where every resulting graph maintains the same singularity status as G. The fold thickness is the maximum length of such a sequence. Building on the NTCBG constructions introduced by Nieva and Nocum (2022), we determine the fold thickness for central fragment trees (Tq), hairy cycles (Hn). Furthermore, we evaluate their extended forms (Tq,m, Hn,m), which are modified structures obtained by iteratively joining the null graph on two vertices K2 to the end-vertices of these central fragments. We also analyze constructed branches derived from K4 and K3,3. By applying graph folding techniques and analyzing adjacency matrix properties, we establish exact values for the fold thickness of these classes. These results provide new algebraic and structural characterizations for NTCBGs.