Original Research Article

Article volume = 2021 and issue = 2

Pages: 160–162

Article publication Date: November, 1, 2021

You can download PDF file of the article here: Download

Visited 27 times and downloaded 7 times

# Break the Symmetry in the Hierarchical Product of an Arbitrary Graph Multiplied by a Path Or a Cycle

#### Tayyebeh Amouzegar

Department of Mathematics, Quchan University of Technology, P.O.Box 94771-67335, Quchan, Iran.

##### Abstract:

In this paper, we investigate the distinguishing number of hierarchical product of an arbitrary graph by a special graph.

##### Keywords:

Distinguishing number, Graph automorphism, Hierarchical product of graphs.

##### References:

- [1] M. O. Albertson and K. L. Collins, Symmetry breaking in graphs, Electron. J. Combin., 3 (1996), no. 1, Research Paper 18, approx. 17 pp. 1
- [2] T. Amouzegar, Distinguishing number of hierarchical products of graphs, Bull. Sci. math., 168 (2021), 102975, https://doi.org/10.1016/j.bulsci.2021.102975. 2, 2.1, 2
- [3] M. Arezoomand and B. Taeri, Applications of generalized hierarchical product of graphs in computing the szeged index of chemical graphs, MATCH Commun. Math. Comput. Chem., 64 (2010) 591–602. 1
- [4] S. E. Andersona, Y. Guob, A. Tenney and K. A. Wash, Prime factorization and domination in the hierarchical product of graphs, Discuss. Math. Graph Theory, 37 (2017) 873–890, doi:10.7151/dmgt.1952. 1
- [5] L. Barri`ere, F. Comellas, C. Dalf´o and M. A. Fiol, The hierarchical product of graphs, Discrete Appl. Math., 157 (2009), 36–48, doi:10.1016/j.dam.2008.04.018. 1
- [6] L. Barri`ere, C. Dalf´ o, M. A. Fiol and M. Mitjana, The generalized hierarchical product of graphs, Discrete Math., 309 (2009), 3871–3881. doi:10.1016/j.disc.2008.10.028. 1
- [7] J. A. Bondy, U. S. R. Murty, Graph Theory, Springer, 2008, GTM 244. 1
- [8] M. Eliasi, A. Iranmanesh, Hosoya polynomial of hierarchical product of graphs, MATCH Commun. Math. Comput. Chem., 69(1) (2013), 111–119. 1
- [9] P. S. Skardal and K. Wash, Spectral properties of the hierarchical product of graphs, Phys. Rev. E 94, 052311 (2016), doi: 10.1103/PhysRevE.94.052311. 1

##### Cite this article as:

- Tayyebeh Amouzegar, Break the Symmetry in the Hierarchical Product of an Arbitrary Graph Multiplied by a Path Or a Cycle, Communications in Combinatorics, Cryptography & Computer Science, 2021(2), PP.160–162, 2021
- Export citation to BibTeX