Some new classes of graceful Lobsters obtained from diameter four trees

Title:

Some new classes of graceful Lobsters obtained from diameter four trees

Creator:

Mishra, Debdas and Panigrahi, Pratima

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:13f39cf4-7596-472f-9395-601cbf56e3f8
uuid:13f39cf4-7596-472f-9395-601cbf56e3f8
doi:10.21136/MB.2010.140703

Subject:

graceful labeling, lobster, odd branch, even branch, inverse transformation, and component moving transformation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We observe that a lobster with diameter at least five has a unique path H = x0, x1, . . . , xm with the property that besides the adjacencies in H both x0 and xm are adjacent to the centers of at least one K1,s, where s > 0, and each xi , 1 ≤ i ≤ m − 1, is adjacent at most to the centers of some K1,s, where s > 0. This path H is called the central path of the lobster. We call K1,s an even branch if s is nonzero even, an odd branch if s is odd and a pendant branch if s = 0. In the existing literature only some specific classes of lobsters have been found to have graceful labelings. Lobsters to which we give graceful labelings in this paper share one common property with the graceful lobsters (in our earlier works) that each vertex xi , 0 ≤ i ≤ m − 1, is even, the degree of xm may be odd or even. However, we are able to attach any combination of all three types of branches to a vertex xi , 1 ≤ i ≤ m, with total number of branches even. Furthermore, in the lobsters here the vertices xi , 1 ≤ i ≤ m, on the central path are attached up to six different combinations of branches, which is at least one more than what we find in graceful lobsters in the earlier works.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

257-278

Source:

Mathematica bohemica | 2010 Volume:135 | Number:3

Harvested from:

CDK

Metadata only:

false