IJPAM: Volume 91, No. 1 (2014)

SOME NEW GRACEFUL GENERALIZED CLASSES
OF LOBSTERS

Debdas Mishra$^1$, Amaresh Chandra Panda$^2$
Department of Mathematics
C.V. Raman College Of Engineering
Bhubaneswar, 752054, INDIA


Abstract. The lobsters with central paths $H = \ x_{0}, x_{1}, \ldots, x_{m}$ to which we give graceful labelings satisfy the following properties.


(i) The vertex $x_{0}$ may be attached to one among the combinations $(e, 0, o)$, $(e, o, e)$, $(e, e, o)$, $(0, o, e)$, $(0, e, o)$.


(ii) The path $H \backslash \{x_{0}\}$ can be partitioned into sub paths $P_{i}, \; 1 \le i \le k$, with the following properties.


(a) The vertices in $P_{i}$ may be attached to at most four different combinations of odd, even, and pendant branches with some restriction on the length of $P_{i}$ and conditions on the number of odd, even, and pendant branches.


(b) Each vertex in $P_{i}$ is attached to an odd (or even) number of branches. If each vertex in $P_{i}$ is attached to a an odd number of branches, then the length of $P_{i}$ is $4$.

Received: October 29, 2013

AMS Subject Classification: 05C78

Key Words and Phrases: graceful labeling, lobster, odd and even branches, component moving transformation

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DOI: 10.12732/ijpam.v91i1.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 1