Volume : 6, Issue : 6, June - 2017

A Note on n-semiregular Graphs

N. Murugesan, R. Anitha

Abstract :

<p>&nbsp;<b style="text-align: justify;"><span lang="EN-IN" style="font-family:&quot;Times New Roman&quot;,serif">A graph in which every vertex has equal number of vertices at distance 2 is called semiregular graph. In particular, if every vertex has exactly n number of vertices at distance 2 then it is called n-semiregular graph. Every regular graph need not be semiregular and vice-versa, but every complete graph is 0-semiregular. In this paper we have constructed semiregular graphs from complete graphs and also we have discussed the n-semiregularity of the well-known graphs (classical graphs) such as circulant graphs and vertex transitive graphs</span></b><b style="text-align: justify;"><span lang="EN-IN" style="font-size:12.0pt;font-family:&quot;Times New Roman&quot;,serif">.</span></b></p> <p class="MsoNormal" style="margin-bottom:0in;margin-bottom:.0001pt;text-align:&#10;justify;line-height:normal"><b><span lang="EN-IN" style="font-size:12.0pt;font-family:&quot;Times New Roman&quot;,serif"><o:p></o:p></span></b></p>