Degree Associated Reconstruction Number of Graphs Obtained by Certain Graph Operations

By : S. Monikandan, A. Anu

Page No: 135-148

Abstract
A vertex-deleted subgraph of a graph G is called a card of G. A card of G with which the degree of the deleted vertex is also given is called a degree associated card (or dacard) of G. The degree associated reconstruction number of a graph G, drn (G), is the size of the smallest collection of dacards of G that uniquely determines G. We show that if G is a disconnected graph whose components are complete graphs, star graphs, cycles or paths, then drn (G) is 2. We also prove that if a hamiltonian graph G of order n contains m set of k nonadjacent vertices of degree n - k, then drn (G) is 1, 2 or 3. Finally, we prove that if G is K2 Pm or Pm[K2] for m > 6, then drn (G) is 2.

Authors :
A. Anu and S. Monikandan : Department of Mathematics Manonmaniam Sundaranar University Tirunelveli - 627 012 Tamilnadu, India.