Extremal unicyclic graphs relative to the sum of the k-power degrees of the graphs

Author(s):

Ali Ghalavand , Mostafa Tavakoli *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

‎Let ‎G ‎be a ‎‎graph ‎and ‎d_G(v) ‎be ‎the ‎degree ‎of v ‎in ‎G‎. Then, the sum of the k-power degrees of ‎‎G ‎is ‎defined ‎as‎ ‎\Sigma_k(G) = \sum_{u \in V(G)}d_G(u)^k‎‎‎. ‎In this paper‎, ‎we obtain a relationship between Stirling number‎, ‎number of trees of subsets and the sum of the k-power degrees of the chemical graphs‎. ‎Also‎, ‎we characterize the extremal unicyclic graphs based on the sum of the k-power degrees of the graphs‎.

Keywords:

Graph , Extremal Problem‎ , ‎Power Degree‎ , ‎Sum Of The Power Degrees‎ , ‎Unicyclic Graph

Language:
Persian
Published:
Soft Computing Journal, Volume:12 Issue: 2, 2025
Pages:
16 to 23
https://www.magiran.com/p2849689  
سامانه نویسندگان
  • Author (1)
    Ali Ghalavand
    Researcher Pure mathematics, Ferdowsi University, Mashhad, Iran
    Ghalavand، Ali
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