In this paper, we define the i-equi-neighbor set and the equi-neighbor polynomial of a graph. Moreover, we find the equi-neighbor polynomial of some graphs.

i-equi-neighbor set, equi-neighbor polynomial

Received: January 29, 2024; Revised: February 8, 2024; Accepted: March 11, 2024; Published: April 5, 2024

How to cite this article: P. Dhanya and V. Anil Kumar, The number of equi-neighbor sets of graphs, Advances and Applications in Discrete Mathematics 41(4) (2024), 281-302. http://dx.doi.org/10.17654/0974165824020

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] K. Priya and V. Anil Kumar, The number of CC-dominating sets of some graphs, South East Asian J. Math. Math. Sci. 19(2) (2023), 211-222.
[2] M. Shikhi and V. Anil Kumar, CNP equivalent classes of graphs, South East Asian J. Math. Math. Sci. 13(2) (2017), 75-84.
[3] M. Shikhi and V. Anil Kumar, On the stability of common neighbor polynomial some graphs, South East Asian J. Math. Math. Sci. 14(1) (2018), 95-102.
[4] M. Shikhi and V. Anil Kumar, Common neighbor polynomial of graphs, Far East J. Math. Sci. (FJMS) 102(6) (2007), 1201-1221.
[5] M. Shikhi and V. Anil Kumar, Common neighbor polynomial of graph operations, Far East J. Math. Sci (FJMS) 102(11) (2017), 2629-2641.
[6] J. Devaraj and E. Sukumaran, On vertex polynomial, International J. of Math. Sci. and Engg. Appls (IJMESA) 6(1) (2012), 371-380.
[7] A. M. Anto and P. Paul Hawkins, Vertex polynomial of graphs with new results, Glob. J. Pure Appl. Math. 15(4) (2019), 469-475.
[8] E. A. Leicht, Petter Holme and M. E. J. Newman, Vertex similarity in networks, Physical Review E 73(2) (2006), 026120.
[9] J. Mycielski, Sur le coloriage des graphes, Colloq. Math. 3 (1955), 161-162.
[10] M. P. Shyama and V. Anil Kumar, Total domination polynomials of complete partite graphs, Advances and Applications in Discrete Mathematics 13 (2014), 23-28.
[11] M. P. Shyama and V. Anil Kumar, On the roots of Hosoya polynomials, J. Discrete Math. Sci. Cryptogr. 19 (2016), 199-219.
[12] E. Sampathkumar and H. B. Walikar, On splitting graph of a graph, Karnataka University Journal XXV (1980), 13-16.
[13] Selvam Avadayappan and M. Bhuvaneshwari, Cosplitting graph and coregular graph, International Journal of Mathematics and Soft Computing 5(1) (2015), 57-64.
[14] R. Ponraj and S. Somasundaram, On the degree splitting graph of a graph, Nat. Acad. Sci. Lett. 27(7 and 8) (2004), 275-278.