On detection number of cycle related graphs

Sanma.G.R; T. Nicholas

doi:https://doi.org/10.14445/22315373/IJMTT-V47P534

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 47 | Number 4 | Year 2017 | Article Id. IJMTT-V47P534 | DOI : https://doi.org/10.14445/22315373/IJMTT-V47P534

On detection number of cycle related graphs

Sanma.G.R, T. Nicholas

Citation :

Sanma.G.R, T. Nicholas, "On detection number of cycle related graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 47, no. 4, pp. 248-252, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V47P534

Abstract

Let G be a connected graph of order n ≥ 3 and let k-labeling c: E(G) → {1, 2, 3, . . . ,k } of the edges of G, (where adjacent edges may be colored the same). For each vertex v of G, the color code of v with respect to c is the k-tuple c(v) = (a1, a2, . . . , ak) where ai is the number of edges incident with v that are colored i (1 ≤ i ≤ k). The k-labeling c is detectable if every two adjacent vertices of G have distinct codes. The minimum positive integer k for which G has a detectable k-labeling is the detection number det(G) of G. In this paper we obtain the detection number of some known graphs such as Pn x Pm, circular halin graph of level two, wheel, crown graph etc.

Keywords

detection number, helm graph, gear graph, wheel, fan, friendship graph.

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