Independent Domination Number for some Special types of Snake Graph

Independent Domination Number for some Special types of Snake Graph N. Senthurpriya S. Meenakshi Abstract
Let G(V, E) be a graph, V has a subset C, contains vertices with atleast one vertex in V that is not in C, then G has the dominating set C. If C has vertices that is not adjacent to one another, then G has an independent dominating set C and so the number of vertices present in the set C represents the IDN, the minimum cardinality of the sets C. In this paper, we were going to deal with Snake graphs in specific, Alternate Triangular and Alternate Quadrilateral Snake graphs. Keeping the concepts of these graphs as our base we extend our paper by defining n-Alternative Triangular Snake graphA(T n ), n-Alternative Double Triangular Snake graph nA(D(T n )), n-Alternative Quadrilateral Snake graphA(Q n ) and n-Alternative Double Quadrilateral Snake graphA(D(Q n )). Further we obtain independent domination number for some special types of snake graphs, in particular n-Alternative Triangular Snake graph nA(T n , n-Alternative Double Triangular Snake graph nA(D(T n )), n-Alternative Double Triangular Snake graph nA(Q n )and n-Alternative Quadrilateral Snake graph and n-Alternative Double Quadrilateral Snake graphA(D(Q n )).
03 01 2021 012218 http://dx.doi.org/10.1088/crossmark-policy iopscience.iop.org Independent Domination Number for some Special types of Snake Graph Journal of Physics: Conference Series paper Published under licence by IOP Publishing Ltd http://creativecommons.org/licenses/by/3.0/ https://iopscience.iop.org/info/page/text-and-data-mining 10.1088/1742-6596/1818/1/012218 https://iopscience.iop.org/article/10.1088/1742-6596/1818/1/012218 https://iopscience.iop.org/article/10.1088/1742-6596/1818/1/012218/pdf https://iopscience.iop.org/article/10.1088/1742-6596/1818/1/012218/pdf https://iopscience.iop.org/article/10.1088/1742-6596/1818/1/012218 https://iopscience.iop.org/article/10.1088/1742-6596/1818/1/012218/pdf Graphs Combin. Kostochka 9 235 1993 10.1007/BF02988312 A cubic 3-connected graph of i (G) can be much larger than its domination number of G Berge 1962 Cockayne 471 1974 Towards a theory of domination in graphs, Networks Cockayne 7 247 1977 The product of the independent domination numbers of a graph and its complement, Discrete Mathematics Cockayne 90 313 1991 Discrete Math. Haviland 307 2643 2007 10.1016/j.disc.2007.01.001 Upper bounds for independent domination in regular graphs Distance two labelling of quadrilateral snake families Baby Smitha 2 283 2016 Discrete Math. Favaron 70 17 1988 10.1016/0012-365X(88)90076-3 Independence and irredundance of parameters with two relations Theory of graphs, Amer. Math. Soc. Transl. Ore 38 206 1962 On independent domination number of regular graphs, Discrete Mathematics Combin Lam 202 135 1999 J. Graph Theory Ao 22 9 1996 10.1002/(SICI)1097-0118(199605)22:1<9::AID-JGT2>3.0.CO;2-S Domination critical graphs with higher independent domination numbers Square difference prime labeling for some snake graphs Sunoj 3 1083 2017 SIAM Journal on Discrete Mathematics Haynes 15 519 2002 10.1137/S0895480100375831 Power domination in graphs applied to electrical power networks Discrete Optim. Shiu 7 86 2010 10.1016/j.disopt.2010.02.004 Large i (G) in Triangle-Free Graphs Ann. Comb. Shiu 16 719 2012 10.1007/s00026-012-0155-4 On the independent domination number of regular graphs Ahrens 1901 IJRTE SenthurPriya X 2019 Independent Domination Number in Triangular and Quadrilateral Snake graphs