Abstract

The Subgraph polynomial fo a graph pair (G, H), where H⫅G, is defined. By assigning particular weights to the variables, it is shown that this polynomial reduces to the dichromatic polynomial of G. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial.

Highlights

  • By assigning particular weights to the variables, it is shown that this polynomial reduces to the dichromatic polynomial of G. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial

  • We will say that an edge e of G is incorporated in G, if it is distinguished in some way and required to belong to every cover K that we consider

  • By applying the theorem recursively, we can obtain an algorithm for finding subgraph polynomials of graph pairs

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Summary

Introduction

By assigning particular weights to the variables, it is shown that this polynomial reduces to the dichromatic polynomial of G. A GENERALIZATION OF THE DICHROMATIC POLYNOMIAL OF A GRAPH The Subgraph polynomial fo a graph pair (G,H), where H G, is defined. This idea of a graph pair leads to a dual generalization of the dichromatic polynomial.

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