This paper is devoted to a study of the concept of edge-group choosability of graphs. We say that G is edge-k-group choosable if its line graph is k-group choosable. In this paper, we study an edge-group choosability version of Vizing conjecture for planar graphs without 5-cycles and for planar graphs without noninduced 5-cycles (2010 Mathematics Subject Classification: 05C15, 05C20).
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