On the spectra of reduced distance matrix of dendrimers

Document Type: Research Paper




Let $G$ be a simple connected graph and $\{v_1,v_2,\ldots‎, ‎v_k\}$ be the set of‎ ‎pendent (vertices of degree one) vertices of $G$‎. ‎The reduced distance matrix of $G$ is a square matrix whose $(i,j)$-entry is the topological distance between $v_i$ and $v_j$ of $G$‎. ‎In this paper‎, ‎we obtain the spectrum‎ ‎of the reduced distance matrix of regular dendrimers‎.


Main Subjects

F. Buckley and F. Harary (1990). Distance in Graphs. Addison-Wesley Publishing Company, Advanced Book Program, Redwood City.
D. H. Rouvray (1986). The role of the topological distance matrix in chemistry. Mathematical and computational concepts in chemistry (Dubrovnik, 1985), Ellis Horwood Ser, Math. Appl., Horwood, Chichester. , 295-306
Z. Mihalic, D. Veljan, D. Amic, S. Nikolic, D. Plavsic and N. Trinajstic (1992). The distance matrix in chemistry. J. Math. Chem.. 11, 223-258
E. A. Smolenskii, E. V. Shuvalova, L. K. Maslova, I. V. Chuvaeva and M. S. Molchanova (2009). Reduced matrix of topological distances with a minimum number of independent parameters: distance vectors and molecular codes. J. Math. Chem.. 45, 1004-1020
B. Horvat, T. Pisanski and M. Randic (2008). Terminal polynomials and star-like graphs. MATCH Commun. Math. Comput. Chem.. 60, 493-512
M. Randic, J. Zupan and D. Vikic-Topic (2007). On representation of proteins by starlike graphs. J. Mol. Graph. Modell.. 26, 290-305
M. Randic and J. Zupan (2004). Highly compact 2D graphical representation of DNA sequences. SAR QSAR Environ. Res. 15, 191-205
M. V. Diudea (1995). Wiener Index of Dendrimers. MATCH Commun. Math.Comput. Chem. 32, 71-83
M. V. Diudea and B. Parv (1995). Molecular Topology. 25. Hyper-Wiener Index of Dendrimers. J. Chem. Inf. Comput. Sci. 35, 1015-1018
A. Heydari (2011). Balaban index of regular dendrimers. Optoelectron. Adv. Mater.-Rapid Commun.. 5 (11), 1260-162
A. Heydari (2010). Harary index of regular dendrimers. Optoelectron. Adv. Mater.-Rapid Commun.. 4 (12), 2206-2208
F. Zhang (1999). Matrix Theory, Basic Results and Techniques. Universitext, Springer-Verlag, New York.