%0 Journal Article
%T Rupture Degree of Some Cartesian Product Graphs
%A Yinkui Li
%A Tingyi Zhu
%J Open Journal of Discrete Mathematics
%P 16-26
%@ 2161-7643
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojdm.2023.131002
%X The
rupture degree of a noncomplete<span><span><span style=\"font-family:;\" \"=\"\">-</span></span></span><span><span><span style=\"font-family:;\" \"=\"\">connected</span></span></span><span><span><span style=\"font-family:;\" \"=\"\"> </span></span></span><span><span><span style=\"font-family:;\" \"=\"\">graph </span></span></span><span><span><i><span style=\"font-family:;\" \"=\"\">G</span></i></span></span><span><span><span style=\"font-family:;\" \"=\"\"> is defined by<img src=\"Edit_992aeb19-aeae-4168-928e-94d0ada5ef37.png\" alt=\"\" /> </span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><br />
</span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span></span><span>, where <img src=\"Edit_4f3aa2ac-1ce6-4ed6-ab39-ceb98493369c.png\" alt=\"\" /></span></span></span></span><span><span><span style=\"font-family:;\" \"=\"\">is the number of components of <img src=\"Edit_b205fd70-cbd3-43fe-a15f-2dbd74bd84bd.png\" alt=\"\" /></span></span></span><span><span><span style=\"font-family:;\" \"=\"\">and <img src=\"Edit_19d0a791-1085-4226-b021-2f31b589f4ef.png\" alt=\"\" /> </span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span></span></span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span> </span>is the order of the l</span></span></span><span><span><span style=\"font-family:;\" \"=\"\">argest component of<img src=\"Edit_0914d59c-688e-4e44-a59a-6a907e773607.png\" alt=\"\" /></span></span></span><span><span><span style=\"font-family:;\" \"=\"\">. In this paper, we
determine the rupture degree of some Cartesian product graphs.</span></span></span>
%K The Rupture Degree
%K Cartesian Product
%K The Vulnerability
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=122369