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Vertex weighted Laplacian graph energy and other topological indices | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 4، دوره 8، شماره 4، اسفند 2023، صفحه 201-209 اصل مقاله (365.6 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2023.524 | ||
| نویسندگان | ||
| Reza Sharafdini* 1؛ Habibeh Panahbar2 | ||
| 1Persian Gulf University | ||
| 2Department of Mathematics, Faculty of Science, Persian Gulf University, Bushehr 7516913817, I. R. Iran | ||
| تاریخ دریافت: 02 آبان 1402، تاریخ بازنگری: 14 آبان 1402، تاریخ پذیرش: 28 آبان 1402 | ||
| چکیده | ||
| Let $G$ be a graph with a vertex weight $omega$ and the vertices $v_1,ldots,v_n$. The Laplacian matrix of $G$ with respect to $omega$ is defined as $L_omega(G)=diag(omega(v_1),cdots,omega(v_n))-A(G)$, where $A(G)$ is the adjacency matrix of $G$. Let $mu_1,cdots,mu_n$ be eigenvalues of $L_omega(G)$. Then the Laplacian energy of $G$ with respect to $omega$ defined as $LE_omega (G)=sum_{i=1}^nbig|mu_i - overline{omega}big|$, where $overline{omega}$ is the average of $omega$, i.e., $overline{omega}=dfrac{sum_{i=1}^{n}omega(v_i)}{n}$. In this paper we consider several natural vertex weights of $G$ and obtain some inequalities between the ordinary and Laplacian energies of $G$ with corresponding vertex weights. Finally, we apply our results to the molecular graph of toroidal fullerenes (or achiral polyhex nanotorus).\[5mm] noindenttextbf{Key words:} Energy of graph, Laplacian energy, Vertex weight, Topological index, toroidal fullerenes. | ||
| کلیدواژه‌ها | ||
| energy of graph؛ Laplacian energy؛ Vertex weight؛ Topological index؛ toroidal fullerenes | ||
| مراجع | ||
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