Irregular Reflexive Labeling and Elementary Row Operations for Enhanced Biometric Image Encryption

A total k-labeling defined the function f_e: E(G) → {1, 2, …, k_e} and f_v: V(G) → {0, 2, …, 2k_v}, where, k = max {k_e, 2k_v}. For graph G, the total k-labeling is called an edge (or a vertex) irregular reflexive k-labeling if the condition of every two different edges (or vertices) has different weights. The smallest value of k for which such labeling exists is called the reflexive edge strength (or reflexive vertex strength) of the graph G, denoted by res (G) (or rvs(G)). This research objective is developing edge irregular reflexive k-labeling and combining edge and vertex irregular reflexive k-labeling and row element operation as an innovative approach to constructing a robust keystream for biometric image encryption. The results show that the best keystream is generated by C_n⊙P₂ and the complete graph. Our results can also surpass existing encryption algorithms such as AES and DES.