International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

The Study of the Number of 2-Matchings in Graphs

Author Affiliations

  • 1Department of mathematics, College of Basic Sciences, Hendijan Branch, Islamic Azad University, Hendijan, IRAN
  • 2Department of Mathematics, College of Basic Sciences, Shahinshar Branch, Islamic Azad University, Shahinshahr, IRAN

Res. J. Recent Sci., Volume 4, Issue (6), Pages 142-143, June,2 (2015)


In this paper we study the 2-matching of finite groups. We use conjugation and character of groups to calculate the number of 2-matchings for some import groups and using them we prove that a finite group G is abelian if and only if the number of its 2-matching is zero.


  1. Williams J., Prime Graph Component of Finite Groups, J. Algebra., 69(2), 487-513 (1981)
  2. Moghadamfar A.R., Shi WJ, Zhou W and Zokayi AR, On the Noncommuting graph Associated with a Finite Group, Siberian mathematical journal, 46(2), 325-332 (2005)
  3. Solmon R. and Wolder A., All Simple Groups are Characterized by their Graphs, Journal of group theory, 16(6), 893-984 (2013)
  4. Darafsheh M.R., Bigdly H. and Bahrami A., Some Results on non Commuting Graph of a Finite Group, Italian J.P.A. Mth., , 107-118 (2010)
  5. Bondy J. A., Murty J. S. R., Graph Theory with Application, Elsevier, (1977)
  6. Williams J.S. , Prime Graph Components of Finite Groups, J. Algebra, 69, 487-513 (1981)
  7. Shah M., Ali A., Ahmad I., An Introduction of new classes of AG-Groupoids, Res. J. recent Sci., 2(1), 67-70, (2013)
  8. Ahmad I., Rashad M. and Shah M., Some New Results on T, T and T4 AG-Groupoids, Res. J. recent Sci., 2(3), 46-66, (2013)
  9. Shah M., Ahmad I. and Ali A., Discovery of new classes of AG-Groupoids, Res. J. recent Sci., 1(11), 47-49, (2012)
  10. Usman M., Iqbal M., Qamar Z. and Shah S. I. A., Structured Equation Models and its Application, Res. J. recent Sci., 3(1), 57-63, (2014)
  11. Mirza N. and Mawal S., Res. J. recent Sci., 2(11), 41-46, (2012)
  12. Vesalian R., Asgari F., Number of 5-Matching in Graphs, Match Commun. Math. Comput. Chem. 69. 33-46,(2013)