The week's pick
Reseach Article
A Characterization of k-Uniform DCSL Graphs
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 125 - Number 7 |
| Year of Publication: 2015 |
| Authors: Nageswara Rao K., Germina K.A., Shaini P. |
10.5120/ijca2015905956
|
Nageswara Rao K., Germina K.A., Shaini P. . A Characterization of k-Uniform DCSL Graphs. International Journal of Computer Applications. 125, 7 ( September 2015), 1-5. DOI=10.5120/ijca2015905956
Abstract
Let an injective function f : V (G) → 2X, where V (G) is the vertex set of a graph G and 2X is the power set of a nonempty set X, be given. Consider the induced function f⊕ : V (G) × V (G) → \{Φ} defined by f⊕ (u, v) = f(u) ⊕ f(v), where f(u) ⊕ f(v) denotes the symmetric difference of the two sets. The function f is called a k-uniform dcsl (and X a k-uniform dcsl-set) of the graph G, if there exists a positive constant k such that |f⊕ (u, v)|= kdG(u, v), where dG(u, v) is the length of a shortest path between u and v in G. If a graph G admits a k-uniform dcsl, then G is called a k-uniform dcsl graph. In this paper, we initiate a study on 2-uniform dscl graphs and we establish a characterization for a graph to be k-uniform dcsl.
References
- Acharya, B. D., 1983, Set-valuations of Graphs and Their Applications. MRI Lecture Notes in Applied Mathematics, No.2, Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad.
- Acharya, B. D., and Germina, K. A., 2011, Distance compatible Set-labeling of Graphs, Indian J. Math. and Comp. Sci. Jhs., 1, 49 - 54.
- Harary, F., 1969, Graph theory, Addison wesley publ. comp. Reading, Massachusetts.
- Germina, K. A., 2012, Uniform Distance-compatible Setlabelings of Graphs, J. of Combinatorics, Information and System Sciences, Vol. 37, 169-178.
- Germina, K. A., and Thomas, B. K., 2011, Distance Compatible Set-Labeling of Graphs, International Mathematical Forum, Vol. 6(31), 1513-1520.
- Thomas, B. K., and Germina, K. A., 2010, (k; r)-Distance Compatible Set-Labeling of Graphs, International Mathematical Forum, Vol. 5(45), 2237-2247.
- Germina, K. A., and Nageswararao, K., 2015, Characterization of Vertex labeling of 1- uniform dcsl graph which form a lattice, Journal of Fuzzy Set Valued Analysis, Vol. 2, 166-170.
- Nageswara Rao, K., and Germina, K. A., 2015, Dimension of Vertex Labeling of k- uniform dcsl path, Advances and Applications in Discrete Mathematics, to appear.
Index Terms
Keywords