A STUDY OF AN UNDIRECTED GRAPH ON A FINITE SUBSET OF NATURAL NUMBERS
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 |
Abstract
Let $G_{n}=(V,E)$ be an undirected simple graph, whose vertex set comprises of the natural numbers which are less than $n$ but not relatively prime to $n$ and two distinct vertices $u,v \in V$ are adjacent if and only if $\gcd(u,v)>1$. Connectedness, completeness, minimum degree, maximum degree, independence number, domination number and Eulerian property of the graph $G_n$ are studied in this paper.
Keywords and Phrases
Clique, connected graph, complete graph, prime counting function.
A.M.S. subject classification
05C07, 05C45, 05C69, 11A05.
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