Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 Seidel energy of a graph with self-loops 757 766 14842 10.22049/cco.2024.29576.2062 EN Harshitha A Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, India - 560064 Sabitha D'Souza Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India, 576104 Swati Nayak Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India, 576104 Ivan Gutman Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia Journal Article 2024 03 19 Let $G_S$ be a graph obtained by attaching a self-loop to each vertex of $S\subseteq V$  of a graph $G(V,E)$. The Seidel matrix of $G_S$ is $S(G_S)=[s_{ij}]$, where $s_{ij}=-1$ if $v_i$ and $v_j$ are adjacent and $v_i\in S$, $s_{ij}=1$ if $v_i$ and $v_j$ are non-adjacent, and it is zero if $i=j$ and $v_i\not\in S$.     If $\theta_i(G_S)\,,\,i=1,2,\ldots,n$, are the eigenvalues of the Seidel matrix, then the Seidel energy of the graph $G_S$, containing $n$ vertices and $\sigma$ self-loops, is defined as $\sum_{i=1}^n \left|\theta_i(G_S)+\frac{\sigma}{n}\right|$. In this paper, some basic properties of Seidel energy of graphs containing self-loops are established. https://comb-opt.azaruniv.ac.ir/article_14842_6d32946bbdfd56c445b722f2d612baa4.pdf