Abstract
This paper deals with decomposition of complete graphs on <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> vertices into circulant graphs with reduced degree <inline-formula> <tex-math notation="LaTeX">r< n-1 </tex-math></inline-formula>. They are denoted as <inline-formula> <tex-math notation="LaTeX">C_{n}(a_{1}, a_{2}, {\dots }, a_{m}) </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">a_{1} </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">a_{m} </tex-math></inline-formula> are generators. Mathematical labeling for such bigger (higher order and huge size) and complex (strictly regular with so many triangles) graphs is very difficult. That is why after decomposition, an edge irregular <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-labeling for these subgraphs is computed with the help of algorithmic approach. Results of <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> are computed by implementing this iterative algorithm in computer. Using the values of <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, an upper bound for edge irregularity strength is suggested for <inline-formula> <tex-math notation="LaTeX">C_{n}(a_{1}, a_{2}, {\dots }, a_{m}) </tex-math></inline-formula> that is <inline-formula> <tex-math notation="LaTeX">{\vert E\vert }/{2}\log _{2} \vert V\vert </tex-math></inline-formula>.