Question

Suppose that are eight knights Alynore, Bedivere, De-gore, Gareth, Kay, Lancelot, Perceval, and Tristan. Their lists of enemies are A (D, G, P), B (K, P, T), D (A, G, L), G (A, D, T), K (B, L, P), L (D, K, T), P (A, B, K), T (B, G, L), where we have represented each knight by the first letter of his name and shown the list of enemies of that knight following this first letter. Draw the graph representing these eight knight and their friends and find a seating arrangement where each knight sits next to two friends.

Short answer

It is a friendship graph.

Step-by-step solution

Given data

There are eight knights Alynore, Bedivere, De-gore, Gareth, Kay, Lancelot, Perceval, and Tristan.

Introduction

Any two compound statements A and B are said to be logically equivalent or simply equivalent if the columns corresponding to A and B in the truth table have identical truth values.

Solution

Here, we use the law of logic.

We have the knights represented by the first letter of their names as:

Alynore =\(A\)

Bedivere =\(B\)

De-gore =\(D\)

Gareth =\(G\)

Kay =\(K\)

Lancelot =\(L\)

Perceval =\(P\)

Tristan =.\(T\)

Using Dirac’s theorem it find that this is a friendship graph.

In this graph each vertex has degree 4, so shall have a Hamilton circuit.

The graph is given below

Hence, it is a friendship graph.