%0 Journal Article
%T (r, 2, r(r   1))-regular graphs
%A N. R. Santhi Maheswari
%A C. Sekar
%J International Journal of Mathematics and Soft Computing
%D 2012
%I SweDha Publication
%X A graph $G$ is called $( r , 2, r ( r - 1) )$-regular if each vertex in the graph $G$ is at a distance one away from exactly $r$ number of vertices and at a distance two away from exactly $r ( r - 1 )$ number of vertices. That is, $d(v) = r$ and $d_2 (v) = r (r-1 )$, for all $v$ in $G$. In this paper, we prove that for any $r > 0$, $r$-regular graph with girth at least five is $(r, 2, r(r-1))$-regular and vice versa and also suggest a method to construct $(r, 2, r(r-1))$-regular graph on $ n imes 2 ^{r-2}$ vertices.
%K Distance degree regular graph
%K $(d
%K k)$-regular graph
%K girth
%K diameter
%K semiregular
%K $(r
%K 2
%K k)$-regular
%U http://ijmsc.com/index.php/ijmsc/article/view/2-2-4/pdf