Hereditary Equality of Domination and Exponential Domination

TL;DR

This paper characterizes a broad class of graphs where the exponential domination number equals the domination number for every induced subgraph, revealing structural properties of these graphs.

Contribution

It provides a characterization of a large subclass of graphs with hereditary equality between exponential and standard domination numbers.

Findings

Identifies conditions under which exponential and domination numbers are equal for all induced subgraphs.

Characterizes a significant subclass of graphs with hereditary domination properties.

Abstract

We characterize a large subclass of the class of those graphs $G$ for which the exponential domination number of $H$ equals the domination number of $H$ for every induced subgraph $H$ of $G$.