On the Minimally Non-outerplanarity of Generalized Middle and Total Graphs

Abstract

Systo and Topp introduced the notions of generalized line, middle and total graphs and they studied the planarity and outerplanarity of these classes of graphs. Conditions under which generalized middle graphs and generalized total graphs are minimally non-outerplanar are discussed in this paper.

Keywords : Planar graphs, middle graphs, total graphs, regular graphs, cocktail party graphs, cliques, cutvertices. 1. Introduction

Let