%0 Journal Article
%T The <i>g</i>-Good-Neighbor Connectivity of Some Cartesian Product Graphs
%A Yinkui Li
%A Ting Xie
%A Xiaoxiao Qin
%J Open Journal of Discrete Mathematics
%P 27-37
%@ 2161-7643
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojdm.2023.131003
%X <p style=\"margin-left:10.0pt;\">
	<span><span style=\"font-family:;\" \"=\"\">The <i>g</i>-good-neighbor connectivity<img src=\"Edit_76b9ddda-fea4-4f68-94a8-aee5cd0c16da.png\" alt=\"\" /> <span></span><span> </span>of <i>G</i> is a generalization of the</span></span><span><span><span style=\"font-family:;\" \"=\"\"> concept of
connectivity<img src=\"Edit_199d0ac4-a9e1-42e0-868f-36f744db9dbe.png\" alt=\"\" />, which is just for<img src=\"Edit_30027f4f-68f0-4cca-bd6b-a161aad9a5d0.png\" alt=\"\" />, and an important parameter in measuring the fault tolerance
and reliability of interconnection network. Many well-known networks can be
constructed by the Cartesian products of some simple graphs. In this paper, we
determine the <i>g</i>-good-neighbor
connectivity of some Cartesian product graphs. We give the exact value of <i>g</i>-good-neighbor connectivity of the
Cartesian product of two <span>complete graphs<img src=\"Edit_21e3003f-ba77-425e-acd6-25adb12c39f1.png\" alt=\"\" /> <span></span><span> </span>and <img src=\"Edit_5a272c12-48cf-44a8-8003-d366411bf775.png\" alt=\"\" /><span></span><span> </span>for <img src=\"Edit_683bf000-7152-4134-8e82-4c0637855e6b.png\" alt=\"\" /><span></span>, mesh<img src=\"Edit_05096ca4-d6ce-44e3-bd33-abe120614889.png\" alt=\"\" /> <span></span><span> </span>for <img src=\"Edit_db3ac97a-3935-4e80-8602-05c25b5fc9d0.png\" alt=\"\" /></span> <span></span>, cylindrical grid<img src=\"Edit_26233fed-9a29-45c9-8561-52b9a2829d19.png\" alt=\"\" /> <span></span><span> </span>and torus <img src=\"Edit_7f520ecc-5bce-4d37-aa06-77ff3a643558.png\" alt=\"\" />for <img src=\"Edit_b41a7d9d-7336-46aa-91f5-0d1d0d6f44e2.png\" alt=\"\" /><span></span>.</span></span></span> 
</p>
%K Connectivity
%K The &lt
%K i&gt
%K g&lt
%K /i&gt
%K -Good-Neighbor Connectivity
%K Cartesian Product
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=122373