The Hub Topological Indices of Graphs
DOI:
https://doi.org/10.26713/cma.v17i3.3177Keywords:
Hub set, Hub Degree of a vertex, Hub Zagreb Index.Abstract
Let G be a simple, connected molecular graph. Topological indices and Hub Parameters
are very important concepts, having wide applications in Chemistry and Networks, respectively.
The hub degree of any vertex of G is the number of minimal hub sets of G containing
v. In this paper, we introduce hub degree based topological indices and establish general
formulae of those indices for some standard graphs, double star graph, book graph. Further
we determine hub Zagreb indices of Join of two noncomplete graphs and molecular graph of
cycloalkenes.
Downloads
References
I. Gutman, Degree-Based Topological Indices, Croat. Chem. Acta, 86(4) (2013), 351 – 361.
I. Gutman and Kinkar Ch. Das, The First Zagreb index 30 years After, MATCH Communications
in Mathematical and in Computer Chemistry, 50 (2004), 83 – 92.
I. Gutman and N. Trinajsti´c, Graph theory and molecular orbitals*. Total π-electron energy
of alternate hydrocarbons, Chemical Physics letters, 17(4) (1972) (535 – 538).
F. Harary, Graph Theory, Addison Wesley, Reading Mass, 1969.
A. M. Hanan Ahmed, Anvar Alwardi, M. Ruby Salestina, On domination topological indices
of graphs, International Journal of Analysis and Applications, 19(1) (2021), 47 – 64.
D. Indriatia, Widodo, I. E. Wijayanti and K. A. Sugeng, On Total Irregularity Strength of
Double-Star and Related Graphs, Procedia Computer Science, 74(2015), 118 – 123.
Ismail Naci Cangul, Aysun Yurttas, Muge Togan and Ahmet Sinan Cevik, Some Formulae
for the Zagreb Indices of Graphs, Numerical Analysis and Applied Mathematics,
(2012), 365 – 367.
S. I. Khalaf and V. Mathad, Restrained hub number in graphs, Bulletin of the International
Mathematical Virtual Institute, 9(2019), 103 – 109.
S. I. Khalaf and V. Mathad, On hubtic and restrained hubtic of a graph, TWMS Journal
of Applied and Engineering Mathematics, 9(4)(2019), 930 – 935.
S. I. Khalaf and V. Mathad,Hub and global hub numbers of a graph, Proc. Jangjeon Math.
Soc., 23(2)(2020), 231 – 239.
S. I. Khalaf, V. Mathad and Sultan Senan Mahde, Hubtic number in graphs, Opuscula
Mathematica, 38(6)(2018), 841 – 847.
R. Khalid, N. Idrees and M. J. Saif, Topological characterization of book graph and stacked
book graph, Computers, Materials Continua, 60(1) (2019) 41 – 54.
S. Nikoli´c, Goran Kova´cevi´c, Ante Mili´cevi´c and Nenad Trinajsti´c, The Zagreb Indices 30
years After, Croat. Chem. Acta., 76(2)(2003), 113 – 124.
V. Mathad, P. Padmapriya and I. N. Cangul, Some topological indices of certain classes of
cycloalkenes, Proceedings of the Jangjeon Mathematical Society, 22(2) (2019), 233 – 247.
M.Walsh, The hub number of a graph, International Journal of Mathematics and Computer
Science, 1, (2006), 117 – 124.




