Generating the Vertex Sets with some Distance Parameter Properties in Caterpillar Graphs

Abstract

In this paper the vertices of caterpillar tree are viewed with different approach and categorized into the sets , and , based on the distance parameters i.e., diameter and radius. The distance parameters have been presented with some set theory views. Here is the set of diametral vertices, is the set of central vertices and is the set of vertices which are neither central nor peripheral. Then, . The cardinality of these sets has some property and helps to specify the basic characters of caterpillar tree. A linear complexity algorithm is also designed to generate these sets.