Exponential Growth of Graph Resolvent

Document Type : Research Paper


Computer Technical Engineering Department, College of Technical Engineering, The Islamic University, Najaf, Iraq and Faculty of Mechanics and Math, Belarusian State University, Belarus


The spectrum of arbitrary graph of finite order the exponential growth of the resolvent of graph G is one of the most investigated object during the last 50 years. In particular, the resolvent matrix is a matrix with property that all of its eigenvalues are outside the spectra of G. In this paper, we study the exponential growth of the resolvent of graph G. The exponential growth of resolvent energy of graph G was investigated.


  1. Gutman, Comparative studies of graph energies, Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math. Natur.) 144 (2012) 1-17.
  2. Gutman, Census of graph energies, MATCH Commun. Math. Comput. Chem. 74 (2015) 219-221.
  3. Shukur and I. Gutman, Energy of monad graphs, Bull. Int. Math. Virtual Inst. 11 (2) (2021) 261-268.
  4. Cvetković, M. Doob and H. Sachs, Spectra of Graphs-Theory and Application, Academic Press, New York, 1980.
  5. S. B. Holland, Introduction to the Theory of Entire Functions, Academic Press-New York and London, 1973.
  6. G. Magaril-Ilyaev and V. M. Tikhomirov, Convex Analysis: Theory and Applications, Translations of Mathematical Monographs, American Mathematical Society, Moscow, Russia, 2003.
  7. Estrada and D. Higham, Network properties revealed through matrix functions, SIAM Rev. 52 (4) (2010) 696-714.
  8. Estrada, Characterization of 3D molecular structure, Chem. Phys. Lett. 319 (5−6) (2000) 713-718.
  9. Gutman, B. Furtula, E. Zogić and E. Glogić, Resolvent of energy of graphs, MATCH Commun. Math. Comput. Chem. 75 (2016) 279-290.
  10. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl. 326 (2007) 1472–1475.
  11. Gutman, B. Furtula, X. Chen and J. Qian, Resolvent Estrada index-computational and mathematical studies, MATCH Commun. Math. Comput. Chem. 74 (2015) 431-440.