آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 125 |
| تعداد مقالات | 1,580 |
| تعداد مشاهده مقاله | 1,735,057 |
| تعداد دریافت فایل اصل مقاله | 1,612,853 |
Seidel energy of a graph with self-loops | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 11، شماره 3، آذر 2026، صفحه 757-766 اصل مقاله (386.69 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29576.2062 | ||
| نویسندگان | ||
| Harshitha A1؛ Sabitha D'Souza* 2؛ Swati Nayak2؛ Ivan Gutman3 | ||
| 1Department of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, India - 560064 | ||
| 2Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India, 576104 | ||
| 3Faculty 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 | ||
|
[1] S. Akbari, J. Askari, and K.C. Das, Some properties of eigenvalues of the seidel matrix, Linear Multilinear Algebra 70 (2022), no. 11, 2150–2161. https://doi.org/10.1080/03081087.2020.1790481
[2] S. Akbari, M. Einollahzadeh, M.M. Karkhaneei, and M.A. Nematollahi, Proof of a conjecture on the seidel energy of graphs, European J. Combin. 86 (2020), Article ID: 103078. https://doi.org/10.1016/j.ejc.2019.103078
[3] D.V. Anchan, S. D’Souza, H.J. Gowtham, and P.G. Bhat, Laplacian energy of a graph with self-loops, MATCH Commun. Math. Comput. Chem. 90 (2023), no. 1, 247–258. https://doi.org/10.46793/match.90-1.247V
[4] M. Biernacki, H. Pidek, and C. Ryll-Nardzewski, Sur une inégalité entre des intégrales définies, Ann. Univ. Mariae Curie-Sklodowska 4 (1950), 1–4.
[5] J.B. Díaz and F.T. Metcalf, Stronger forms of a class of inequalities of G. Pólya-G. Szegö, and L.V. Kantorovich, Bull. Am. Math. Soc. 69 (1963), 415–418.
[6] M. Einollahzadeh and M.A. Nematollahi, An improved lower bound for the seidel energy of trees, Discrete Appl. Math. 320 (2022), 381–386. https://doi.org/10.1016/j.dam.2022.06.012
[7] I. Gutman, I. Redžepović, B. Furtula, and A. Sahal, Energy of graphs with self-loops, MATCH Commun. Math. Comput. Chem. 87 (2022), 645–652.
[8] I. Jovanović, E. Zogić, and E. Glogić, On the conjecture related to the energy of graphs with self-loops, MATCH Commun. Math. Comput. Chem. 89 (2023), no. 2, 479–488. https://doi.org/10.46793/match.89-2.479J
[9] X. Li, Y. Shi, and I. Gutman, Graph Energy, Springer, New York, 2012.
[10] B.J. McClelland, Properties of the latent roots of a matrix: The estimation of π-electron energies, J. Chem. Phys. 54 (1971), no. 2, 640–643. https://doi.org/10.1063/1.1674889
[11] M.R. Oboudi, Energy and seidel energy of graphs, MATCH Commun. Math. Comput. Chem. 75 (2016), 291–303.
[12] M.R. Oboudi and M.A. Nematollah, Improving a lower bound for seidel energy of graphs, MATCH Commun. Math. Comput. Chem. 89 (2023), no. 2, 489–502. https://doi.org/10.46793/match.89-2.489O
[13] K.M. Popat and K.R. Shingala, Some new results on energy of graphs with self loops, J. Math. Chem. 61 (2023), no. 6, 1462–1469. https://doi.org/10.1007/s10910-023-01467-7
[14] U.P. Preetha, M. Suresh, and E. Bonyah, On the spectrum, energy and laplacian energy of graphs with self-loops, Heliyon 9 (2023), no. 7, #e17001. https://doi.org/10.1016/j.heliyon.2023.e17001 | ||
|
آمار تعداد مشاهده مقاله: 835 تعداد دریافت فایل اصل مقاله: 984 |
||