We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

The Total Irregularity of Some Composite Graphs

by Hosam Abdo, Darko Dimitrov
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 122 - Number 21
Year of Publication: 2015
Authors: Hosam Abdo, Darko Dimitrov
10.5120/21846-5170

Hosam Abdo, Darko Dimitrov . The Total Irregularity of Some Composite Graphs. International Journal of Computer Applications. 122, 21 ( July 2015), 1-9. DOI=10.5120/21846-5170

@article{ 10.5120/21846-5170,
author = { Hosam Abdo, Darko Dimitrov },
title = { The Total Irregularity of Some Composite Graphs },
journal = { International Journal of Computer Applications },
issue_date = { July 2015 },
volume = { 122 },
number = { 21 },
month = { July },
year = { 2015 },
issn = { 0975-8887 },
pages = { 1-9 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume122/number21/21846-5170/ },
doi = { 10.5120/21846-5170 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:11:06.254636+05:30
%A Hosam Abdo
%A Darko Dimitrov
%T The Total Irregularity of Some Composite Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 122
%N 21
%P 1-9
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The total irregularity of a simple undirected graph G = (V;E) is defined as irrt(G) = 1 2 P u;v2V (G) jdG(u) ?? dG(v)j, where dG(u) is the degree of the vertex u. In this paper we investigate the change of the total irregularity of graphs under various subdivision operations. Also, we present exact expressions and upper bounds on the total irregularity of different composite graphs such as the double graph, the extended double cover of a graph, the generalized thorn graph, several variants of subdivision corona graphs, and the hierarchical product graphs.

References
  1. H. Abdo, S. Brandt, and D. Dimitrov. The total irregularity of a graph. Discrete Math. Theor. Comput. Sci. , 16:201–206, 2014.
  2. H. Abdo and D. Dimitrov. The irregularity of graphs under graph operations. Discuss. Math. Graph Theory, 34:263–278, 2014.
  3. H. Abdo and D. Dimitrov. The total irregularity of graphs under graph operations. Miskolc Math. Notes, 15:3–17, 2014.
  4. M. Albertson. The irregularity of a graph. Ars Comb. , 46.
  5. N. Alon. Eigenvalues and expanders. Combinatorica, 6:83– 96, 1986.
  6. L. Barri´ere, F. Comellas, C. Dalf´o, and M. Fiol. The hierarchical product of graphs. Discrete Appl. Math. , 157:36–48, 2009.
  7. F. Bell. A note on the irregularity of graphs. Linear Algebra Appl. , 161:45–54, 1992.
  8. D. Bonchev and D. Klein. On the wiener number of thorn trees, stars, rings, and rods. Croat. Chem. Acta, 75:613–620, 2002.
  9. N. De. Augmented eccentric connectivity index of some thorn graphs. Intern. J. Appl. Math. Res. , 1:671–680, 2012.
  10. N. De. On eccentric connectivity index and polynomial of thorn graph. Appl. Math. , 3:931–934, 2012.
  11. N. De, A. Pal, and S. Nayeem. Modified eccentric connectivity of generalized thorn graphs. Intern J. Computational Math. , 2014. http://dx. doi. org/10. 1155/2014/436140.
  12. T. Dehghan-Zadeh, H. Hua, A. Ashrafi, and N. Habibi. Remarks on a conjecture about randi c index and graph radius. Miskolc Math. Notes, 14:845–850, 2013.
  13. D. Dimitrov and R. ?Skrekovski. Comparing the irregularity and the total irregularity of graphs. Ars Math. Contemp, 9:45– 50, 2015.
  14. I. Gutman. Distance in thorny graph. Publ. Inst. Math. , 63:31– 36, 1998.
  15. P. Hansen and H. M´elot. Variable neighborhood search for extremal graphs 9. bounding the irregularity of a graph. DIMACS Ser. Discrete Math. Theoret. Comput. Sci. , 69:253– 264, 1962.
  16. A. Heydari and I. Gutman. On the terminal wiener index of thorn graphs. Kragujevac J. Science, 32:57–64, 2010.
  17. H. Hua, S. Zhang, and K. Xu. Further results on the eccentric distance sum. Discrete Appl. Math. , 160.
  18. K. Kathiresan and C. Parameswaran. Certain generalized thorn graphs and their wiener indices. J. Appl. Math. Informatics, 30:793–807, 2012.
  19. X. Liu and P. Lub. Spectra of subdivision-vertex and subdivision-edge neighbourhood corona. Linear Algebra Appl. , 438:3547–3559, 2013.
  20. P. Lu and Y. Miao. Spectra of the subdivision-vertex and subdivision-edge corona. arXiv:1302. 0457v2.
  21. H. Walikar, H. Ramane, L. Sindagi, S. Shirakol, and I. Gutman. Hosoya polynomial of thorn trees, rods, rings, and stars. Kragujevac J. Science, 28:47–56, 2006.
  22. B. Zhou. On modified wiener indices of thorn trees. Kragujevac J. Math. , 27:5–9, 2005.
  23. B. Zhou and D. Vuki?cevi?c. On wiener-type polynomials of thorn graphs. J. Chemometrics, 23:600–604, 2009.
Index Terms

Computer Science
Information Sciences

Keywords

irregularity of a graph total irregularity of a graph graph invariants composite graphs

Powered by PhDFocusTM