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General Randic matrix and general Randic energy | ||
| Transactions on Combinatorics | ||
| مقاله 3، دوره 3، شماره 3، آذر 2014، صفحه 21-33 اصل مقاله (356.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2014.5451 | ||
| نویسندگان | ||
| Ran Gu1؛ Fei Huang2؛ Xueliang Li* 3 | ||
| 1Center for Combinatorics, nankai University, Tianjin, China | ||
| 2Center for Combinatorics, Nankai University, Tianjin, China | ||
| 3Center for Combinatorics, Nankai University, Tianjin 300071, China | ||
| چکیده | ||
| Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$ and $d_i$ the degree of its vertex $v_i$, $i = 1, 2, \dots, n$. Inspired by the Randic matrix and the general Randic index of a graph, we introduce the concept of general Randi'c matrix $\textbf{R}_\alpha$ of $G$, which is defined by $(\textbf{R}_\alpha)_{i,j}=(d_id_j)^\alpha$ if $v_i$ and $v_j$ are adjacent, and zero otherwise. Similarly, the general Randic eigenvalues are the eigenvalues of the general Randic} matrix, the greatest general Randic eigenvalue is the general Randic spectral radius of $G$, and the general Randic energy is the sum of the absolute values of the general Randic eigenvalues. In this paper, we prove some properties of the general Randi'c matrix and obtain lower and upper bounds for general Randic energy, also, we get some lower bounds for general Randic spectral radius of a connected graph. Moreover, we give a new sharp upper bound for the general Randic energy when $\alpha=-1/2$. | ||
| کلیدواژهها | ||
| general Randic matrix؛ general Randic energy؛ eigenvalues؛ spectral radius | ||
| مراجع | ||
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B. Bollob\'{a}s and P. Erd\H{o}s (1998) Graphs of extremal weights Ars Combin. 50, 225-233
J. A. Bondy and U. S. R. Murty (2008) Graph Theory Springer New York 244
\c{S}. B. Bozkurt, A. D. G\"{u}ng\"{o}r and I. Gutman (2010) Randi\'{c} spectral radius and Randi\'{c} energy MATCH Commun. Math. Comput. Chem. 64, 321-334
S. B. Bozkurt, A. D. Gongor, I. Gutman and A. S. Cevik (2010) Randi\'c Matrix and Randi\'c Energy MATCH Commun. Math. Comput. Chem. 64, 239-250
D. Cvetkovic, M. Doob and H. Sachs (1980) Spectra of Graphs--Theory and Application Academic Press, New York 87
M. Cavers, S. Fallat and S. Kirkland (2010) On the normalized Laplacian energy and general Randi\'{c} index $R_{-1}$ of graphs Linear Algebra Appl. 433, 172-190
B. Furtula and I. Gutman (2013) Comparing energy and Randi\'c energy Macedonian Journal of Chemistry and Chemical Engineering 32 (1), 117-123
F. R. Gantmacher (1959) The Theory of Matrices Chelsea, New York
I. Gutman, B. Furtula and \c{S}. B. Bozkurt (2014) On Randi\' c energy Linear Algebra Appl. 442, 50-57
C. Godsil and G. Royle (2001) Algebraic Graph Theory Springer, New York
M. Randi\'{c} (1975) On characterization of molecular branching J. Amer. Chem. Soc. 97, 6609-6615
L. Shi (2009) Bounds on Randi\'{c} indices Discrete Math. 309 (16), 5238-5241
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