Öz, Mert SinanCangül, İsmail Naci2024-09-182024-09-182022-01-010037-8712https://doi.org/10.5269/bspm.47918https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/47918https://hdl.handle.net/11452/44905In this paper, the determinant of the sum-edge adjacency matrix of any given graph without loops is calculated by means of an algebraic method using spanning elementary subgraphs and also the coefficients of the corresponding sum-edge characteristic polynomial are determined by means of the elementary subgraphs. Also, we provide a formula for calculating the number of smallest odd-sized cycles in a given regular graph.eninfo:eu-repo/semantics/openAccessEnergyGraphsAdjacencySum-edge adjacencyCharacteristic polynomialPermutationScience & technologyPhysical sciencesMathematicsArticle4010.5269/bspm.479182175-1188