Extremal Unicyclic Graphs With Minimal Distance Spectral Radius

• Autorzy: Hongyan Lu , Jing Luo , Zhongxun Zhu
• Języki publikacji: EN

Abstrakty

EN

The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m ≠ 3). In this paper, we determine the extremal unicyclic graph which has minimal distance spectral radius in U (n,m) \ Cn.

Słowa kluczowe

EN

distance matrix; distance spectral radius; unicyclic graph; matching.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 4
• Strony: 735-749

Daty

wydano

2014-11-01

otrzymano

2012-08-06

poprawiono

2013-05-15

zaakceptowano

2013-11-04

online

2014-11-15

Twórcy

autor

Hongyan Lu

• College of Mathematics and Statistics South Central University for Nationalities Wuhan 430074, P.R. China

autor

Jing Luo

• College of Mathematics and Statistics South Central University for Nationalities Wuhan 430074, P.R. China

autor

Zhongxun Zhu

• College of Mathematics and Statistics South Central University for Nationalities Wuhan 430074, P.R. China

Bibliografia

• [1] A.T. Balaban, D. Ciubotariu and M. Medeleanu, Topological indices and real number vertex invariants based on graph eigenvalues or eigenvectors, J. Chem. Inf. Comput. Sci. 31 (1991) 517-523. doi:10.1021/ci00004a014
• [2] R.B. Bapat, Distance matrix and Laplacian of a tree with attached graphs, Linear Algebra Appl. 411 (2005) 295-308. doi:10.1016/j.laa.2004.06.017
• [3] R.B. Bapat, S.J. Kirkland and M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005) 193-209. doi:10.1016/j.laa.2004.05.011
• [4] B. Bollob´as, Modern Graph Theory (Springer-Verlag, 1998). doi:10.1007/978-1-4612-0619-4
• [5] V. Consonni and R. Todeschini, New spectral indices for molecule description, MATCH Commun. Math. Comput. Chem. 60 (2008) 3-14.
• [6] I. Gutman and M. Medeleanu, On the structure-dependence of the largest eigenvalue of the distance matrix of an alkane, Indian J. Chem. (A) 37 (1998) 569-573.
• [7] A. Ilić, Distance spectral radius of trees with given matching number , Discrete Appl. Math. 158 (2010) 1799-1806. doi:10.1016/j.dam.2010.06.018
• [8] G. Indulal, Sharp bounds on the distance spectral radius and the distance energy of graphs, Linear Algebra Appl. 430 (2009) 106-113. doi:10.1016/j.laa.2008.07.005
• [9] Z. Liu, On spectral radius of the distance matrix , Appl. Anal. Discrete Math. 4 (2010) 269-277. doi:10.2298/AADM100428020L
• [10] D. Stevanović and A. Ili´c, Distance spectral radius of trees with fixed maximum degree, Electron. J. Linear Algebra 20 (2010) 168-179.
• [11] G. Yu, Y. Wu, Y. Zhang and J. Shu, Some graft transformations and its application on a distance spectrum, Discrete Math. 311 (2011) 2117-2123. doi:10.1016/j.disc.2011.05.040
• [12] X. Zhang and C. Godsil, Connectivity and minimal distance spectral radius, Linear Multilinear Algebra 59 (2011) 745-754. doi:10.1080/03081087.2010.499512
• [13] B. Zhou, On the largest eigenvalue of the distance matrix of a tree, MATCH Com- mun. Math. Comput. Chem. 58 (2007) 657-662.
• [14] B. Zhou and N. Trinajsti´c, On the largest eigenvalue of the distance matrix of a connected graph, Chem. Phys. Lett. 447 (2007) 384-387. doi:10.1016/j.cplett.2007.09.048

Identyfikatory

DOI

10.7151/dmgt.1772