Debdas Mishra ¹, Sushant Kuma Rout ², Purna Chandra Nayak ³

Affiliations
1 C. V. Raman College of Engineering, Bidyanagar, Mahura, Janla, Bhubaneswar – 752 054, Orissa,, IN
2 College of Engineering and Technology, Ghatikia, Kalinga Nagar, Bhubaneswar – 751003, Odisha,, IN
3 Bhadrak (Autonomous) College, Jaganathpur, Baudpur Village, Bhadrak, Odisha – 756100,, IN

Abstract

The objective of this article is to give graceful labeling to some new classes of lobsters in a bid to resolve the three and half decade old Bermond’s conjecture that all lobsters are graceful. Here we use the method of component moving transformation such as the transfer of the first and second type and the derived transformations such as BD8TF, 1JTF, and 2JTF for generating graceful trees from a given one. In a bid to resolve Bermond’s conjecture here we give graceful labelings to many classes of lobsters possessing at least one of the two distinct features from those found in the literature as detailed below. 1.The central paths of the lobsters contain one or more vertices which do not have any neighbour apart from those on the central path. 2.One or more vertices of the central paths are attached to leaves. 3. The vertices on the central path may be attached to any of the fifteen different combination of odd, even, and pendant branches.

Keywords

AMS classification: 05C78, BD8TF, Graceful Labeling, Lobster, Odd and Even Branches, Transfers of the First and Second Type, 1JTF, 2JTF

Full Text

   

Rajakishore Samal ¹, Debdas Mishra ²

Affiliations
1 Department of Mathematics, O.P.S.Mohavidyalaya, Hindol Road, Dhenkanal – 759019, Odisha, IN
2 Department of Mathematics, C.V.Raman College of Engineering and Technology, Bhubaneswar – 752054, Odisha, IN

Abstract

Objectives: To explore and identify some new classes of graphs which exhibit polygonal sum labeling. Methods: In this article we use a methodology which fundamentally involves formulation and subsequent mathematical validation. Findings: Here we establish that the graphs – Star ( K_1,n ), Coconut Tree, Bistar (S_m,n), the Graph S _{m n k} Comb, (P _n K ₁) and Subdivision graph S(K _1,n) admit pentagonal, hexagonal, heptagonal, octagonal, nonagonal and decagonal sum labeling. Applications: One can explore to generalize these results and extend to give n-gonal labeling to some classes graphs. Sum labeling has already been used in the problems involving relational database management and hence one can try out to use polygonal sum labeling as well in these problems.

Keywords

Bistar, Coconut Tree, Comb, Polygonal Sum Labeling, Star, Subdivision Graph.

Full Text