A STUDY ON HARMONIOUS COLORING OF SNAKE DERIVED ARCHITECTURE

Abstract

There are only few graphs which gives the precise value of the harmonious chromatic number. There are only few results concerning about this problem. We give the precise value of harmonious chromatic number of central graph of snake derived architecture. In this article, we find the harmonious chromatic number of central graph of snake derived architecture using the maximum degree of this architecture and the detailed proof of this is given by induction process. Further we have observed the Maximum matching number of this architecture and it is denoted bya’(𝐺). Using these observations and theorem we have characterized the maximum matching number and edge covering problem of these architecture with harmonious chromatic number χℎ (𝐺).

Keywords

• Harmonious colouring
• Snake graph
• Matching
• Perfect matching
• Edge covering
• Central graph