Abstract
The distance matrix of a simple graph G is \(D(G)=(d_{i,j})\), where \(d_{i,j}\) is the distance between the ith and jth vertices of G. The distance spectral radius of G, written \(\lambda _{1}(G)\), is the largest eigenvalue of D(G). We determine the distance spectral radius of the wheel graph \(W_{n}\), a particular type of spider graphs, and the generalized Petersen graph P(n, k) for \(k\in \{2,3\}\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Balaban, A.T., Ciubotariu, D., Medeleanu, M.: Topological indices and real number vertex invariants based on graph eigenvalues or eigenvectors. J. Chem. Inf. Comput. Sci. 31, 517–523 (1991)
Balasubramanian, K.: A topological analysis of the \(C_{60}\) buckminsterfullerene and \(C_{70}\) based on distance matrices. Chem. Phys. Lett. 239, 117–123 (1995)
Bapat, R.B.: Distance matrix and Laplacian of a tree with attached graphs. Linear Algebra Appl. 411, 295–308 (2005)
Bapat, R.B., Kirkland, S.J., Neumann, M.: On distance matrices and Laplacians. Linear Algebra Appl. 401, 193–209 (2005)
Bose, S.S., Nath, M., Paul, S.: Distance spectral radius of graphs with r pendent vertices. Linear Algebra Appl. 435, 2828–2836 (2011)
Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Springer, New York (2011)
Consonni, V., Todeschini, R.: New spectral indices for molecule description. MATCH Commun. Math. Comput. Chem. 60, 3–14 (2008)
Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs-Theory and Applications. Academic Press, New York (1980)
Das, K.C.: On the largest eigenvalue of the distance matrix of a bipartite graph. MATCH Commun. Math. Comput. Chem. 62, 667–672 (2009)
Fowler, P.W., Caporossi, G., Hansen, P.: Distance matrices, wiener indices, and related invariants of fullerenes. J. Phys. Chem. A 105, 6232–6242 (2001)
Gutman, I., Medeleanu, M.: On the structure-dependence of the largest eigenvalue of the distance matrix of an alkane. Indian J. Chem. A 37, 569–573 (1998)
Ilic̃, A.: Distance spectral radius of trees with given matching number. Discrete Appl. Math. 158(16), 1799–1806 (2010)
Indulal, G.: Sharp bounds on the distance spectral radius and the distance energy of graphs. Linear Algebra Appl. 430, 106–113 (2009)
Minc, H.: Nonnegative Matrices. John Wiley & Sons, New York (1988)
Nath, M., Paul, S.: On the distance spectral radius of bipartite graphs. Linear Algebra Appl. 436, 1285–1296 (2012)
Nath, M., Paul, S.: On the distance spectral radius of trees. Linear and Multilinear Algebra 61, 847–855 (2013)
Stevanovic̃, D., Ilic̃, A.: Distance spectral radius of trees with fixed maximum degree. Electron. J. Linear Algebra 20(1), 168–179 (2010)
Subhi, R., Powers, D.: The distance spectrum of the path \(P_{n}\) and the first distance eigenvector of connected graphs. Linear and Multilinear Algebra 28, 75–81 (1990)
Todeschini, R., Consonni, V.: Handbook of Molecular Descriptors. Wiley-VCH, Weinheim (2000)
Zhou, B.: On the largest eigenvalue of the distance matrix of a tree. MATCH Commun. Math. Comput. Chem. 58, 657–662 (2007)
Zhou, B., Trinajstic̃, N.: On the largest eigenvalue of the distance matrix of a connected graph. Chem. Phys. Lett. 447, 384–387 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Atik, F., Panigrahi, P. (2016). Distance Spectral Radius of Some k-partitioned Transmission Regular Graphs. In: Govindarajan, S., Maheshwari, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2016. Lecture Notes in Computer Science(), vol 9602. Springer, Cham. https://doi.org/10.1007/978-3-319-29221-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-29221-2_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29220-5
Online ISBN: 978-3-319-29221-2
eBook Packages: Computer ScienceComputer Science (R0)