Maximum signless Laplacian Estrada index of tetracyclic graphs

In this study, we aim to determine the unique tetracyclic graph that maximizes the signless Laplacian Estrada index (SLEE) among all tetracyclic graphs. The SLEE of a graph ? is defined as the sum of the exponentials of its eigenvalues, expressed as follows: SLEE(?)=?n,i=1 esi, where s1, s2,...,sn are the eigenvalues of the signless Laplacian matrix of ?. By identifying this unique tetracyclic graph, we desire to understand the specific structural characteristics that contribute to the maximum SLEE within the class of tetracyclic graphs.