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Specifically, we show that a Leavitt path algebra $L$ over an arbitrary graph $E$ is a graded $\\Sigma $-$V$ ring if and only if it is a subdirect product of matrix rings of arbitrary size but with finitely many non-zero entries over $K$ or $K[x,x^{-1}]$ with appropriate matrix gradings. We also obtain a graphical characterization of such a graded $\\Sigma $-$V$ ring $L$% . 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