%0 Journal Article
%T The Generalization of Signed Domination Number of Two Classes of Graphs
%A Xia Hong
%A Guoyan Ao
%A Feng Gao
%J Open Journal of Discrete Mathematics
%P 114-132
%@ 2161-7643
%D 2021
%I Scientific Research Publishing
%R 10.4236/ojdm.2021.114009
%X Let <img src=\"Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png\" width=\"58\" height=\"20\" alt=\"\" /> be a graph. A function <img src=\"Edit_b7158ed5-6825-41cd-b7f0-5ab5e16fc53d.png\" width=\"79\" height=\"20\" alt=\"\" /> is said to be a Signed Dominating Function (SDF) if <img src=\"Edit_c6e63805-bcaa-46a9-bc77-42750af8efd4.png\" width=\"135\" height=\"25\" alt=\"\" /> holds for all <img src=\"Edit_bba1b366-af70-46cd-aefe-fc68869da670.png\" width=\"42\" height=\"20\" alt=\"\" />. The signed domination number <img src=\"Edit_22e6d87a-e3be-4037-b4b6-c1de6a40abb0.png\" width=\"284\" height=\"25\" alt=\"\" />. In this paper, we determine the exact value of the Signed Domination Number of graphs <img src=\"Edit_36ef2747-da44-4f9b-a10a-340c61a3f28c.png\" width=\"19\" height=\"20\" alt=\"\" /> and <img src=\"Edit_26eb0f74-fcc2-49ad-8567-492cf3115b73.png\" width=\"19\" height=\"20\" alt=\"\" /> for <img src=\"Edit_856dbcc1-d215-4144-b50c-ac8a225d664f.png\" width=\"32\" height=\"20\" alt=\"\" />, which is generalized the known results, respectively, where <img src=\"Edit_4b7e4f8f-5d38-4fd0-ac4e-dd8ef243029f.png\" width=\"19\" height=\"20\" alt=\"\" /> and <img src=\"Edit_6557afba-e697-4397-994e-a9bda83e3219.png\" width=\"19\" height=\"20\" alt=\"\" /> are denotes the <em>k</em>-th power graphs of cycle <img src=\"Edit_27e6e80f-85d5-4208-b367-a757a0e55d0b.png\" width=\"21\" height=\"20\" alt=\"\" /> and path <img src=\"Edit_70ac5266-950b-4bfd-8d04-21711d3ffc33.png\" width=\"18\" height=\"20\" alt=\"\" />.
%K Signed Domination Function
%K Signed Domination Numbers
%K Graphs C&lt
%K sub&gt
%K n&lt
%K /sub&gt
%K &lt
%K sup style=&quot
%K margin-left:-7px
%K &quot
%K &gt
%K k&lt
%K /sup&gt
%K Graphs P&lt
%K sub&gt
%K n&lt
%K /sub&gt
%K &lt
%K sup style=&quot
%K margin-left:-7px
%K &quot
%K &gt
%K k&lt
%K /sup&gt
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=112729