In this paper we show that a tree T with the following properties have graceful labeling. 1] T ha... more In this paper we show that a tree T with the following properties have graceful labeling. 1] T has a path H such that every pendant vertex of T has distance n (a fixed positive integer) from H. 2] Every vertex of T excluding one end vertex of H has even degree.
Study on Harmonious Labeling of Symmetrical Trees of Diameter Four
Current Topics on Mathematics and Computer Science Vol. 3
A harmonious labeling on a graph G is an injection from the vertices of G to the group of integer... more A harmonious labeling on a graph G is an injection from the vertices of G to the group of integers modulo k, where k is the number of edges of G, that induces a bijection between the edges of G and the numbers modulo k by taking the edge label for an edge ab to be the sum of the labels of the two vertices a\(\cong\)b(modk).In this paper we prove that the symmetrical trees of diameter four admit harmonious labeling. Harmonious graphs can be used in the study of error correcting codes and channel assignment problems.
We observe that a lobster with diameter at least five has a unique path (called the central path)... more We observe that a lobster with diameter at least five has a unique path (called the central path) such that and are adjacent to the centers of at least one where , and besides adjacencies in the central path each , is at most adjacent to the centers of some .We call an odd branch if is odd , an even branch if is non-zero even, and a pendant branch if . In this paper we give graceful labeling to some new classes of lobsters with each vertex of the central path is attached to an even number of branches. Furthermore the branches incident on the central path are either even branches or some combinations of even and pendant branches.
The lobsters with central paths H = x0, x1, . . . , xm to which we give graceful labelings satisf... more The lobsters with central paths H = x0, x1, . . . , xm to which we give graceful labelings satisfy the following properties. (i) The vertex x0 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\{x0} can be partitioned into sub paths Pi, 1 ≤ i ≤ k, with the following properties. (a) The vertices in Pi may be attached to at most four different combinations of odd, even, and pendant branches with some restriction on the length of Pi and conditions on the number of odd, even, and pendant branches. (b) Each vertex in Pi is attached to an odd (or even) number of branches. If each vertex in Pi is attached to a an odd number of branches, then the length of Pi is 4. AMS Subject Classification: 05C78
A class of graceful lobsters with even number of branches incident on the central path
... Amaresh Chandra Panda graceful. Bermond's conjecture is also open and very few ... more ... Amaresh Chandra Panda graceful. Bermond's conjecture is also open and very few classes of lobsters are known to be graceful. Ng [10], Wang et al. [13], Chen et al. [2] , Morgan [9] (see [3]), and Mishra and Panigrahi[4,5,6,7,8,11] have given graceful labeling to some classes ...
In this paper we show that a tree T with the following properties have graceful labeling. 1] T ha... more In this paper we show that a tree T with the following properties have graceful labeling. 1] T has a path H such that every pendant vertex of T has distance n (a fixed positive integer) from H. 2] Every vertex of T excluding one end vertex of H has even degree.
International Journal of Pure and Apllied Mathematics, 2014
The lobsters with central paths H = x 0 , x 1 ,. .. , x m to which we give graceful labelings sat... more The lobsters with central paths H = x 0 , x 1 ,. .. , 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\{x 0 } can be partitioned into sub paths P i , 1 ≤ i ≤ 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.
A Class Of Graceful Lobsters with even number of branches incident on the central path
ijmsa.yolasite.com
... Amaresh Chandra Panda graceful. Bermond's conjecture is also open and very few ... more ... Amaresh Chandra Panda graceful. Bermond's conjecture is also open and very few classes of lobsters are known to be graceful. Ng [10], Wang et al. [13], Chen et al. [2] , Morgan [9] (see [3]), and Mishra and Panigrahi[4,5,6,7,8,11] have given graceful labeling to some classes ...
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