Öz, Mert SinanCangul, Ismail Naci2024-06-072024-06-0720220037-87122175-1188https://hdl.handle.net/20.500.12885/2241In 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.enginfo:eu-repo/semantics/openAccessGraphsAdjacencySum-edge adjacencyCharacteristic polynomialPermutationarticle10.5269/bspm.4791840WOS:000841490400038Q2