Threat, support and dead edges in the Shannon game

TL;DR

This paper explores the concepts of captured vertices and dead edges in the Shannon game using graph theory, providing simple methods to identify these elements and simplify the complex analysis of the game.

Contribution

It introduces straightforward techniques for detecting dead edges and captured vertex sets, aiding in the analysis of the Shannon game.

Findings

Methods for identifying dead edges

Techniques for detecting captured vertices

Simplification of Shannon game analysis

Abstract

The notions of captured/lost vertices and dead edges in the Shannon game (Shannon switching game on nodes) are examined using graph theory. Simple methods are presented for identifying some dead edges and some captured sets of vertices, thus simplifying the (computationally hard) problem of analyzing the game.