10.11575/CDM.V15I3.68174
Behtoei, Ali
Khatibi, Mahsa
Attarzadeh, Fatemeh
Degree sequence of the generalized Sierpiński graph
Contributions to Discrete Mathematics
2020
2019-04-30
2020-02-04
2020-12-24
2020-12-22
en
Article
110-5235-68174
10.11575/cdm.v15i3
88-97 Pages
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Sierpiński graphs are studied in fractal theory and have applications in diverse areas including dynamic systems, chemistry, psychology, probability, and computer science. Polymer networks and WK-recursive networks can be modeled by generalized Sierpiński graphs. The degree sequence of (ordinary) Sierpi\'nski graphs and Hanoi graphs (and some of their topological indices) are determined in the literature. The number of leaves (vertices of degree one) of the generalized Sierpiński graph $S(T, t)$ of any tree $T$ was determined in 2017 and in terms of $t$, $|V(T)|$, and the number of leaves of the base graph $T$. In this paper, we generalize these results. More precisely, for every simple graph $G$ of order $n$, we completely determine the degree sequence of the generalized Sierpiński graph $S(G,t)$ of $G$ in terms of $n$, $t$ and the degree sequence of $G$. By using it, we determine the exact value of the general first Zagreb index of $S(G,t)$ in terms of the same parameters of $G$.
Contributions to Discrete Mathematics, Vol. 15 No. 3 (2020)