Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2026 01 08 On generalized commutative Leonardo quaternions and their generalization 15090 10.22049/cco.2026.30871.2653 EN Hasan Gökbaş Department of Mathematics, University of Bitlis Eren, Bitlis, Turkey Anetta Szynal-Liana Department of Discrete Mathematics, Rzeszow University of Technology, Rzeszów, Poland Journal Article 2025 08 04 In this paper, we give some properties of the generalized commutative Leonardo quaternions, among others the Binet formula, generating function, and the general bilinear index-reduction formula which imply d'Ocagne, Vajda, Halton, Catalan, and Cassini identities. We also give the matrix representations and some sum formulas of the generalized commutative Leonardo quaternions. Moreover, we present a one-parameter generalization of the generalized commutative Leonardo quaternions and their properties.  https://comb-opt.azaruniv.ac.ir/article_15090_6f9da1ef80ff524b2aeed776b0ae1fb7.pdf