Butterfly Graphs with Shell Orders m and 2m+1 are Graceful
Journal Title: Bonfring International Journal of Research in Communication Engineering - Year 2012, Vol 2, Issue 2
Abstract
A graceful labelling of an un directed graph G with n edges is a one-one function from the set of vertices V(G) to the set {0, 1, ,2, . . ., n} such that the induced edge labels are all distinct. An induced edge label is the absolute difference between the two end vertex labels. A shell graph is defined as a cycle Cn with (n -3) chords sharing a common end point called the apex . A double shell is one vertex union of two shells. A bow graph is defined to be a double shell in which each shell has any order. In this paper we define a butterfly graph as a bow graph with exactly two pendant edges at the apex and we prove that all butterfly graphs with one shell of order m and the other shell of order (2m + 1) are graceful.
Authors and Affiliations
Ezhilarasi Hilda Stanley , Jeba Jesintha J
Keywords
Related Articles
- EP ID EP114736
- DOI 10.9756/BIJRCE.1245
- Views 131
- Downloads 0
Design and Development of Gaussian Minimum Shift Keying (GMSK) Demodulator for Satellite Communication
This paper discusses DSP based implementation of Gaussian Minimum Shift Keying (GMSK) demodulator using Polarity type Costas loop. The demodulator consists of a Polarity type Costas loop for carrier recovery, data recove...
Comparison of Cellular Automata and DSP Processors towards DSP Application
In this paper we have emphasized on alternative uses of Cellular Automata (CA) in Digital Signal Processing (DSP). The corollary of the distinction is centered on the parallel nature for both of the processors. For digit...
A Systematic Study on Cyber Physical System
Cyber-physical systems (CPSs) are physical and engineered systems whose operations are monitored, coordinated, controlled and integrated by a computing and communication core. The economic and societal potential of such...
Data Integrity and Dynamic Storage Way in Cloud Computing Resonance and Parametric Analysis of Planar Broad-Wall Longitudinal Slot Array Antennas
It is not an easy task to securely maintain all essential data where it has the need in many applications for clients in cloud. To maintain our data in cloud, it may not be fully trustworthy because client doesn?t have c...
Opportunistic Channel Access Algorithm Based on Hidden Semi Markov Model for Cognitive Radio Networks
Future generation cellular networks highly depend on Cognitive radio due to its capability to handle the primary user channel utilization. However, channel sensing and allocation for secondary user are the major factors...