Vol. 16 No. 3 (2017): Mapana Journal of Sciences
Research Articles

Path (or cycle)-trees with Graph Equations involving Line and Split Graphs

H P Patil
Pondicherry University
V Raja
Pondicherry University
Bio

Published 2017-05-10

Abstract

H-trees generalizes the existing notions of trees, higher dimensional trees and k-ctrees. The characterizations and properties of both Pk-trees for k at least 4 and Cn-trees for n at least 5 and their hamiltonian property, dominations, planarity, chromatic and b-chromatic numbers are established. The conditions under which Pk-trees for k at least 3 (resp. Cn-trees for n at least 4), are the line graphs are determined. The relationship between path-trees and split graphs are developed.