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Some remarks on the sum of the inverse values of the normalized signless Laplacian eigenvalues of graphs | ||
Communications in Combinatorics and Optimization | ||
دوره 6، شماره 2، اسفند 2021، صفحه 259-271 اصل مقاله (411.56 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2021.26987.1173 | ||
نویسندگان | ||
Igor Milovanovic* 1؛ Emina Milovanovic2؛ Marjan Matejic2؛ Serife Burcu Bozkurt Altındağ3 | ||
1Faculty of Electronic Engineering, Nis, Serbia | ||
2Faculty of Electronic Engineering | ||
3Yenikent Kardelen Konutlari, Selcuklu | ||
چکیده | ||
Let $G=(V,E)$, $V=\{v_1,v_2,\ldots,v_n\}$, be a simple connected graph with $n$ vertices, $m$ edges and a sequence of vertex degrees $d_1\geq d_2\geq\cdots\geq d_n>0$, $d_i=d(v_i)$. Let ${A}=(a_{ij})_{n\times n}$ and ${D}=\mathrm{diag}d_1,d_2,\ldots , d_n)$ be the adjacency and the diagonal degree matrix of $G$, respectively. Denote by ${\mathcal{L}^+}(G)={D}^{-1/2} (D+A) {D}^{-1/2}$ the normalized signless Laplacian matrix of graph $G$. The eigenvalues of matrix $\mathcal{L}^{+}(G)$, $2=\gamma _{1}^{+}\geq \gamma_{2}^{+}\geq \cdots \geq \gamma_{n}^{+}\geq 0$, are normalized signless Laplacian eigenvalues of $G$. In this paper some bounds for the sum $K^{+}(G)=\sum_{i=1}^n\frac{1}{\gamma _{i}^{+}}$ are considered. | ||
کلیدواژهها | ||
Laplacian matrix؛ normalized signless Laplacian matrix؛ eigenvalues | ||
مراجع | ||
[1] Ş.B. Bozkurt Altındağ, Note on the sum of powers of normalized signless Laplacian eigenvalues of graphs, Math. Interdisc. Res. 4 (2019), no. 2, 171–182.
[2] Ş.B. Bozkurt Altındağ, Sum of powers of normalized signless Laplacian eigenvalues and Randić (normalized) incidence energy of graphs, Bull. Inter. Math. Virtual Inst. 11 (2021), no. 1, 135–146.
[3] Ş.B. Bozkurt Altındağ, A.D. Güngör, I. Gutman, and A.S. Çevik, Randić matrix and Randić energy, MATCH Commun. Math. Comput. Chem. 64 (2010), no. 1, 239–250.
[4] S. Butler, Algebraic aspects of the normalized Laplacian, in: Recent Trends in Combinatorics, IMA Vol. Math. Appl. 159, Springer, 2016, pp. 295–315.
[5] M. Cavers, S. Fallat, and S. Kirkland, On the normalized Laplacian energy and general Randi´c index R−1 of graphs, Lin. Algebra Appl. 433 (2010), no. 1, 172–190.
[6] B. Cheng and B. Liu, The normalized incidence energy of a graph, Lin. Algebra Appl. 438 (2013), no. 11, 4510–4519.
[7] F.R.K. Chung, Spectral Graph Theory, no. 92, Amer. Math. Soc. Providence, 1997.
8] D. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs, Academic press, New York, 1980.
[9] K.C. Das, A.D. Gungor, and Ş.B. Bozkurt Altındağ, On the normalized Laplacian eigenvalues of graphs, Ars Combin. 118 (2015), 143–154.
[10] Z. Du, A. Jahanbani, and S.M. Sheikholeslami, Relationships between Randi´c index and other topological indices, Commun. Comb. Optim. 6 (2021), no. 1, 137–154.
[11] S. Furuichi, On refined Young inequalities and reverse inequalities, J. Math. Inequal. 5 (2011), 21–31.
[12] R. Gu, F. Huang, and X. Li, Randić incidence energy of graphs, Trans. Comb. 3 (2014), no. 4, 1–9.
[13] J.G. Kemeny and J.L. Snel, Finite Markov Chains, Van Nostrand, Princeton, N.J., 1960.
[14] M. Levene and G. Loizou, Kemeny’s constant and the random surfer, Amer. Math. Monthly 109 (2002), no. 8, 741–745.
[15] J. Li, J.-M. Guo, and W.C. Shiu, Bounds on normalized Laplacian eigenvalues of graphs, J. Inequal. Appl. 2014 (2014), no. 1, ID: 316.
[16] M. Matejić, I. Milovanović, and E. Milovanović, Remarks on the degree Kirchoff index, Kragujevac J. Math. 43 (2019), no. 1, 15–21.
[17] E.I. Milovanović, M.M. Matejić, and I.Z. Milovanović, On the normalized Laplacian spectral radius, Laplacian incidence energy and Kemeny’s constant, Lin. Algebra Appl. 582 (2019), 181–196.
[18] D.S. Mitrinović and P.M. Vasić, Analytic Inequalities, Springer Verlag, BerlinHeidelberg-New York, 1970.
[19] M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), no. 23, 6609–6615.
[20] S. Sun and K.C. Das, On the second largest normalized Laplacian eigenvalue of graphs, Appl. Math. Comput. 348 (2019), 531–541.
[21] B. Zhou and N. Trinajstić, On resistance-distance and Kirchhoff index, J. Math. Chem. 46 (2009), no. 1, 283–289.
[22] P. Zumstein, Comparison of spectral methods through the adjacency matrix and the Laplacian of a graph, Th. Diploma, ETH Z¨urich, 2005. | ||
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