VERTEX CUT POLYNOMIALS OF SOME UNARY GRAPH OPERATIONS

Abstract

Let $G=(V, E)$ be a simple undirected graph of order $n, V(G, i)$ be the family of vertex cuts with cardinality $i$ and $d_v(G, i)=|V(G, i)|$. Then the vertex cut polynomial of $G$ is defined as
$$
V[G ; x]=\sum_{i=\kappa(G)}^{n-2} d_v(G, i) x^i .
$$

In this paper, we focus on vertex cut polynomials of some unary graph operations.

Received: August 5, 2022;
Revised: January 18, 2023;
Accepted: January 31, 2023;