Equitable partition and star set formulas for the subgraph centrality of graphs

ABSTRACT

Let G be an undirected graph with adjacency matrix $A\left(G\right)$. For a vertex $u\in V\left(G\right)$, the subgraph centrality of u in G is $C_S\left(u\right)=(\exp (A\left(G\right)){)}_{uu}=\sum _{k=0}^{\mathrm{\infty }}\frac{1}{k!}(A(G{)}^k{)}_{uu}$. In this paper, we give some formulas for $C_S\left(u\right)$ by using equitable partitions and star sets of G.

Keywords:

• Subgraph centrality
• adjacency matrix
• equitable partition
• star set

2010 Mathematics Subject Classification:

• 05C50

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11801115 and 12071097], the Natural Science Foundation of the Heilongjiang Province [grant number QC2018002] and the Fundamental Research Funds for the Central Universities.