Abstract

A complete bipartite graph $K_{1,n}$ is called a star. A decomposition $\mathcal{D} =\{G_1,G_2,\cdots,G_{t}\}$ of a connected graph $G=(\mathcal{V}, \mathcal{E})$, which is ordered, is a star resolving $t$-decomposition for $G$, if it is a resolving decomposition and each $G_l,1\leq l \leq t$, is a star. If $t$ is the minimum positive integer sugh that $G$ has a star resolving $t$-decomposition, then $t$ is called the star decomposition dimension of $G$, denoted by $sdec(G)$. In this paper, star decomposition dimension of some class of graphs are determined.

Keywords and Phrases

Graph Decomposition, Decomposition Dimension, Resolving Decomposition, Connected Decomposition Number, Star Decomposition Dimension.

A.M.S. subject classification

05C38, 05C76, 05C12.

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