\input zb-basic \input zb-ioport \iteman{io-port 05360240} \itemau{Arumugam, S.; Meena, S.} \itemti{Common weight decomposition into minimum acyclic graphoidal covers.} \itemso{Acharya, B. D. (ed.) et al., Labelings of discrete structures and applications. New Delhi: Narosa Publishing House (ISBN 978-81-7319-860-1/hbk). 69-76 (2008).} \itemab A difference labeling of a graph $G=(V,E)$ is an injection $f$ from $V$ to a set of non-negative integers together with a weight function $g_f$ on $E$ defined as $g_f(uv) = \vert f(u)-f(v)\vert$ for every $uv \in E$. A decomposition of $G$ into parts such that each part contains the edges having a common weight is called a common weight decomposition. An acyclic graphoidal cover is a collection $\psi$ of paths in $G$ whose edge sets partition the edge set $E$ of $G$. The existence of minimum graphoidal covers which are common weight decompositions is proved for trees, unicyclic graphs, connected graphs in which every block is a cycle, certain hamiltonian graphs, and corona graphs $K_{n,n} \circ K_1$. \itemrv{Dalibor Fron\v cek (Duluth)} \itemcc{} \itemut{graphoidal cover; acyclic graphoidal cover; difference labeling; common weight decomposition} \itemli{} \end