Ascending domination decomposition of subdivision of graphs

K Lakshmiprabha, K Nagarajan

Abstract


In this paper, the two major fields of graph theory namely decomposition and domination are connected and new concept called Ascending Domination Decomposition ($ADD$) of a graph $G$ is introduced. An $ADD$ of a graph $G$ is a collection $\psi=\{G_{1},G_{2},\ldots,G_{n}\}$ of subgraphs of $G$ such that, each $G_{i}$ is connected, every edge of $G$ is in exactly one $G_{i}$ and $\gamma(G_{i})=i$, $1\leq i\leq n$. In this paper, we prove the subdivision of some standard graphs admit $ADD$.

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References


Y. Alavi, A. J. Boals, G. Chartrand, P. Erdos and O. R. Oellermann, The

Ascending Subgraph Decomposition Problem, Cong. Number., 8(1987), 7 -

G. Chartrand and L. Lesniak, Graphs and Digraphs, Chapman Hall CRC.

(2004).

F. Harary, Graph Theory, Addison - Wesley publishing Company Inc, USA,

(1969).

Juraj Bosak, Decomposition of Graphs, Kluwer Academic Publishers, 1990.

K. Lakshmiprabha and K. Nagarajan, Ascending Domination

Decomposition of Graphs, International Journal of Mathematics and

Soft Computing. Vol.4,No.1(2014), 199 - 128.

K. Lakshmiprabha and K. Nagarajan, Ascending Domination

Decomposition of Some Special Graphs, Proceedings of the National seminar

on Current Trends in Mathematics, S. B. K. College, Aruppukkottai. February,

(2014).

H. B. Walikar, B. D. Acharya and E. Sampathkumar, Recent developements

in the theory of domination in graphs MRI Lecture Notes No 1, ,The Mehta

Research Institute (1979).


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