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Seidel energy of a graph with self-loops | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 شهریور 1403 اصل مقاله (386.68 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29576.2062 | ||
| نویسندگان | ||
| Harshitha A1؛ Sabitha D'Souza* 1؛ Swati Nayak1؛ Ivan Gutman2 | ||
| 1Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India, 576104 | ||
| 2Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Seidel energy (of graph), Seidel matrix؛ energy (of graph), graph with self-loops | ||
| مراجع | ||
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