%0 Journal Article
%T New Results on One Modulo N-Difference Mean Graphs
%A Pon Jeyanthi
%A Meganathan Selvi
%A Damodaran Ramya
%J Open Journal of Discrete Mathematics
%P 100-112
%@ 2161-7643
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojdm.2023.134010
%X A graph <i>G</i> is said to be one modulo N-difference mean graph if there is an
injective function <i>f</i> from the vertex
set of <i>G</i> to the set<img src=\"Edit_93f011e8-e37b-46aa-8399-2a358cc48190.png\" alt=\"\" /> <span><span><span style=\"font-family:;\" \"=\"\"><br />
</span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span></span><span>, where <i>N</i> is the natural number and <i>q</i> is the number of edges of <i>G</i> and <i>f</i></span></span></span></span><span><span><span style=\"font-size:12.0pt;font-family:;\" \"=\"\"> </span></span></span><span><span><span style=\"font-family:;\" \"=\"\">induces
a bijection&nbsp;<img src=\"Edit_059de6cb-6911-4e54-8c26-d2b95ef76e51.png\" alt=\"\" /> <span></span><span> </span>from the edge set of <i>G</i> to<img src=\"Edit_7b31c334-7d4e-4590-8602-c055a04c600a.png\" alt=\"\" /></span></span></span><span><span><span style=\"font-family:;\" \"=\"\"> <span></span><span> </span>given by<img src=\"Edit_6473c37c-a009-48b8-bace-57259c30916c.png\" alt=\"\" /> <span></span><span> </span>and the function <i>f</i> is called a one modulo N-difference
mean labeling of <i>G</i>. In this paper, we
show that the graphs such as arbitrary union of paths,<img src=\"Edit_f49b4eb9-d4b3-467c-9078-40c63b69171d.png\" alt=\"\" /> <span></span>, ladder, slanting ladder, diamond snake, quadrilateral snake,
alternately quadrilateral snake,<img src=\"Edit_4dbfeee9-05b7-4cf2-9b6a-b6a6470ed028.png\" alt=\"\" /> <span></span>,<img src=\"Edit_c557249b-6f79-40ee-ad01-d67696ed6677.png\" alt=\"\" /> <span></span>,<img src=\"Edit_529f2eb2-478a-4c30-8c36-27959b5c8a97.png\" alt=\"\" /> <span></span>,<img src=\"Edit_12f0e816-d89f-4691-871f-1c95610d45a8.png\" alt=\"\" /> <span></span>, friendship graph and<img src=\"Edit_0e4ac5aa-a848-41c7-8596-851dad483804.png\" alt=\"\" /> </span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><br />
</span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span></span><span> </span>admit one modulo
N-difference mean labeling.</span></span></span>
%K Skolem Difference Mean Labeling
%K One Modulo N-Graceful Labeling
%K One Modulo N-Difference Mean Labeling and One Modulo N-Difference Mean Graph
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=128474