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Note on degree Kirchhoff index of graphs | ||
| Transactions on Combinatorics | ||
| مقاله 5، دوره 2، شماره 3، آذر 2013، صفحه 43-52 اصل مقاله (318.74 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2013.3288 | ||
| نویسندگان | ||
| Mardjan Hakimi-Nezhaad1؛ Ali Reza Ashrafi1؛ Ivan Gutman* 2 | ||
| 1University of Kashan | ||
| 2University of Kragujevac Kragujevac, Serbia | ||
| چکیده | ||
| The degree Kirchhoff index of a connected graph $G$ is defined as the sum of the terms $d_i\,d_j\,r_{ij}$ over all pairs of vertices, where $d_i$ is the degree of the $i$-th vertex, and $r_{ij}$ the resistance distance between the $i$-th and $j$-th vertex of $G$. Bounds for the degree Kirchhoff index of the line and para-line graphs are determined. The special case of regular graphs is analyzed. | ||
| کلیدواژه‌ها | ||
| resistance distance (in graphs)؛ Kirchhoff index؛ degree Kirchhoff index؛ spectrum of graph؛ Laplacian spectrum of graph | ||
| مراجع | ||
|
R. B. Bapat, I. Gutman and W. Xiao (2003) A simple method for computing resistance distance Z. Naturforsch. 58a, 494-498
J. A. Bondy and U. S. R. Murty (1976) Graph theory
with applications American Elsevier Publishing Co., Inc., New York
N. Biggs (1993) Algebraic graph theory Second edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge
S. Bozkurt and D. Bozkurt (2012) On the sum of powers
of normalized Laplacian eigenvalues of graphs MATCH Commun. Math. Comput. Chem. 68, 917-930
S. Butler (2008) Eigenvalues and structures of graphs Ph. D. Thesis, University of California, San Diego
M. Cavers, S. Fallat and S. Kirkland (2010) On the
normalized Laplacian energy and general Randic index
R_{-1} of graphs Linear Algebra Appl. 433, 172-190
F. R. K. Chung (1997) Spectral graph theory Am. Math.
Soc., Providence
H. Chen and F. Zhang (2007) Resistance distance and the
normalized Laplacian spectrum Discrete Appl. Math. 155, 654-661
K. C. Das, A. D. Gungor and S. B. Bozkurt On the normalized Laplacian eigenvalues of graphs Ars Combin., in press
X. Gao, Y. Luo and W. Liu (2012) Kirchhoff index in line,
subdivision and total graphs of a regular graph Discrete Appl. Math. 160, 560-565
I. Gutman and B. Mohar (1996) The Quasi--Wiener and the Kirchhoff indices coincide J. Chem. Inf. Comput. Sci. 36, 982-985
G. H. Hardy, J. E. Littlewood and G. Polya (1988) Inequalities Cambridge Univ. Press, Cambridge
D. J. Klein and M. Randi\'c (1993) Resistance distance J. Math. Chem. 12, 81-95
J. L. Palacios (2001) Resistance distance in graphs and
random walks Int. J. Quantum Chem. 81, 29-33
J. L. Palacios (2001) Closed--form formulas for
Kirchhoff index Int. J. Quantum Chem. 81, 135-140
J. L. Palacios (2013) Upper and lower bounds for the
additive degree--Kirchhoff index MATCH Commun.
Math. Comput. Chem. 70, 651-655
J. Palacios and J. M. Renom (2011) Another look at the
degree Kirchhoff index Int. J. Quantum Chem. 111, 3453-3455
W. Xiao and I. Gutman (2003) On resistance matrices MATCH Commun. Math. Comput. Chem. 49, 67-81
W. Xiao and I. Gutman (2003) Resistance distance and
Laplacian spectrum Theor. Chem. Acc. 110
W. Xiao and I. Gutman (2004) Relations between resistance and
Laplacian matrices and their applications MATCH Commun. Math. Comput. Chem. 51, 119-127
W. Yan, Y. N. Yeh and F. Zhang (2012) The asymptotic
behavior of some indices of iterated line graphs
of regular graphs Discrete Appl. Math. 160, 1232-1239
F. J. Zhang, Y. C. Chen and Z. B. Chen (2009) Clique-inserted
graphs and spectral dynamics of clique--inserting J. Math. Anal. Appl. 349, 211-225
H. Zhang, Y. Yang and C. Li (2009) Kirchhoff index of
composite graphs Discrete Appl. Math. 157, 2918-2927
B. Zhou and N. Trinajstic (2008) A note on Kirchhoff
index Chem. Phys. Lett. 455, 120-123
B. Zhou and N. Trinajstic (2009) On resistance--distance
and Kirchhoff index J. Math. Chem. 46, 283-289
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