Coronas and domination subdivision number of a graph

TL;DR

This paper introduces a new graph operation called the general corona based on vertex neighborhood partitions and uses it to characterize trees with a domination subdivision number of 3.

Contribution

It defines the general corona operation on graphs and applies it to characterize specific trees based on domination subdivision number.

Findings

Introduces the general corona operation for graphs.

Provides a characterization of trees with domination subdivision number 3.

Establishes properties of the new graph operation.

Abstract

In this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G \circ P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.