Multi-level distance labelings for the prism related graphs $D^{p}_{n}$

Saima Nazeer, Imrana Kousar

Abstract


Let $G$ be a connected graph with diameter diam$(G)$ and $d(x,y)$ denotes the distance between any two distinct vertices $x$, $y$ in $G$. A radio labeling $f$ of $G$ is an assignment of non negative integer to the vertices of $G$ satisfying $|f(x)-f(y)|\geq $diam$(G)-d(x,y)+1$. The span of a radio labeling is the maximum integer assigned to a vertex. The radio number of $G$ denoted by rn$(G)$, is the minimum possible span. In this paper, we determine the radio number for the prism related graphs, $D_{n}^{p}$ when $n=4k+2$.

Full Text:

PDF

References


M. Ali, M.T. Rahim, G. Ali, On two families of graphs with constant metric dimension, Journal

of Prime Research in Mathematics, Volume 8,(2012), 95-101.

G. Chartrand, D. Erwin, P. Zhang, F. Harary, Radio labelings of graphs, Bull. Inst. Combin.

Appl., 33 (2001), 7785.

C. Fernandez, A. Flores, M. Tomova, C. Wyels, The radio number of gear graphs, Preprint

arxive: 0809. 2623VI [Math. Co], 15 Sep 2008.

M. T. Rahim, M. Farooq, M. Ali, S. Jan, Multilevel distance labelings for generalized gear graphs,

International Journal of Mathematics and Soft Computing Vol.2, No. 1 (2012), 57-63.


Refbacks

  • There are currently no refbacks.




Web Counters

IJMSC has been indexed in several world class data bases like Google Scholar, DRJI (Directory of Research Journals Indexing) ,Cite Factor, Research Bible.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.