| Summary: | <p class="p1">Let <em>G</em> be a simple and finite graph. A graph is said to be <em>decomposed</em> into subgraphs <em>H</em><sub>1</sub> and <em>H</em><sub>2</sub> which is denoted by <em>G</em> = <em>H</em><sub>1</sub> ⊕ <em>H</em><sub>2</sub>, if <em>G</em> is the edge disjoint union of <em>H</em><sub>1</sub> and <em>H</em><sub>2</sub>. If <em>G</em> = <em>H</em><sub>1</sub> ⊕ <em>H</em><sub>2</sub> ⊕ <em>H</em><sub>3</sub> ⊕ ... ⊕ <em>H<sub>k</sub></em>, where <em>H</em><sub>1</sub>, <em>H</em><sub>2</sub>, <em>H</em><sub>3</sub>, ..., <em>H<sub>k</sub></em> are all isomorphic to <em>H</em>, then <em>G</em> is said to be <em>H</em>-decomposable. Futhermore, if <em>H</em> is a cycle of length <em>m</em> then we say that <em>G</em> is <em>C<sub>m</sub></em>-decomposable and this can be written as <em>C<sub>m</sub></em>|<em>G</em>. Where <em>G</em> × <em>H</em> denotes the tensor product of graphs <em>G</em> and <em>H</em>, in this paper, we prove the necessary and sufficient conditions for the existence of <em>C</em><sub>4</sub>-decomposition of <em>K<sub>m</sub></em> × <em>K<sub>n</sub></em>. Using these conditions it can be shown that every even regular complete multipartite graph <em>G</em> is<span class="Apple-converted-space"> <em>C</em><sub>4</sub>-</span>decomposable if the number of edges of <em>G</em> is divisible by 4. <span class="Apple-converted-space"> </span></p>
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