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A Characterization of k-Uniform DCSL Graphs

by Nageswara Rao K., Germina K.A., Shaini P.
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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

@article{ 10.5120/ijca2015905956,
author = { Nageswara Rao K., Germina K.A., Shaini P. },
title = { A Characterization of k-Uniform DCSL Graphs },
journal = { International Journal of Computer Applications },
issue_date = { September 2015 },
volume = { 125 },
number = { 7 },
month = { September },
year = { 2015 },
issn = { 0975-8887 },
pages = { 1-5 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume125/number7/22441-2015905956/ },
doi = { 10.5120/ijca2015905956 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:15:22.319204+05:30
%A Nageswara Rao K.
%A Germina K.A.
%A Shaini P.
%T A Characterization of k-Uniform DCSL Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 125
%N 7
%P 1-5
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
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
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  3. Harary, F., 1969, Graph theory, Addison wesley publ. comp. Reading, Massachusetts.
  4. Germina, K. A., 2012, Uniform Distance-compatible Setlabelings of Graphs, J. of Combinatorics, Information and System Sciences, Vol. 37, 169-178.
  5. Germina, K. A., and Thomas, B. K., 2011, Distance Compatible Set-Labeling of Graphs, International Mathematical Forum, Vol. 6(31), 1513-1520.
  6. Thomas, B. K., and Germina, K. A., 2010, (k; r)-Distance Compatible Set-Labeling of Graphs, International Mathematical Forum, Vol. 5(45), 2237-2247.
  7. 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.
  8. 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

Computer Science
Information Sciences

Keywords

k-uniform distance compatible set-labeling k-uniform dcsl index

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