Call for Paper - January 2023 Edition
IJCA solicits original research papers for the January 2023 Edition. Last date of manuscript submission is December 20, 2022. Read More

The Total Irregularity of Some Composite Graphs

Print
PDF
International Journal of Computer Applications
© 2015 by IJCA Journal
Volume 122 - Number 21
Year of Publication: 2015
Authors:
Hosam Abdo
Darko Dimitrov
10.5120/21846-5170

Hosam Abdo and Darko Dimitrov. Article: The Total Irregularity of Some Composite Graphs. International Journal of Computer Applications 122(21):1-9, July 2015. Full text available. BibTeX

@article{key:article,
	author = {Hosam Abdo and Darko Dimitrov},
	title = {Article: The Total Irregularity of Some Composite Graphs},
	journal = {International Journal of Computer Applications},
	year = {2015},
	volume = {122},
	number = {21},
	pages = {1-9},
	month = {July},
	note = {Full text available}
}

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

  • H. Abdo, S. Brandt, and D. Dimitrov. The total irregularity of a graph. Discrete Math. Theor. Comput. Sci. , 16:201–206, 2014.
  • H. Abdo and D. Dimitrov. The irregularity of graphs under graph operations. Discuss. Math. Graph Theory, 34:263–278, 2014.
  • H. Abdo and D. Dimitrov. The total irregularity of graphs under graph operations. Miskolc Math. Notes, 15:3–17, 2014.
  • M. Albertson. The irregularity of a graph. Ars Comb. , 46.
  • N. Alon. Eigenvalues and expanders. Combinatorica, 6:83– 96, 1986.
  • L. Barri´ere, F. Comellas, C. Dalf´o, and M. Fiol. The hierarchical product of graphs. Discrete Appl. Math. , 157:36–48, 2009.
  • F. Bell. A note on the irregularity of graphs. Linear Algebra Appl. , 161:45–54, 1992.
  • D. Bonchev and D. Klein. On the wiener number of thorn trees, stars, rings, and rods. Croat. Chem. Acta, 75:613–620, 2002.
  • N. De. Augmented eccentric connectivity index of some thorn graphs. Intern. J. Appl. Math. Res. , 1:671–680, 2012.
  • N. De. On eccentric connectivity index and polynomial of thorn graph. Appl. Math. , 3:931–934, 2012.
  • 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.
  • 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.
  • D. Dimitrov and R. ?Skrekovski. Comparing the irregularity and the total irregularity of graphs. Ars Math. Contemp, 9:45– 50, 2015.
  • I. Gutman. Distance in thorny graph. Publ. Inst. Math. , 63:31– 36, 1998.
  • 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.
  • A. Heydari and I. Gutman. On the terminal wiener index of thorn graphs. Kragujevac J. Science, 32:57–64, 2010.
  • H. Hua, S. Zhang, and K. Xu. Further results on the eccentric distance sum. Discrete Appl. Math. , 160.
  • K. Kathiresan and C. Parameswaran. Certain generalized thorn graphs and their wiener indices. J. Appl. Math. Informatics, 30:793–807, 2012.
  • X. Liu and P. Lub. Spectra of subdivision-vertex and subdivision-edge neighbourhood corona. Linear Algebra Appl. , 438:3547–3559, 2013.
  • P. Lu and Y. Miao. Spectra of the subdivision-vertex and subdivision-edge corona. arXiv:1302. 0457v2.
  • 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.
  • B. Zhou. On modified wiener indices of thorn trees. Kragujevac J. Math. , 27:5–9, 2005.
  • B. Zhou and D. Vuki?cevi?c. On wiener-type polynomials of thorn graphs. J. Chemometrics, 23:600–604, 2009.