Partially normal 5-edge-colorings of cubic graphs

In a proper edge-coloring of cubic graph, an edge e is normal if the set colors used by five edges incident with end has cardinality 3 or 5. The Petersen coloring conjecture asserts that every bridgeless graph 5-edge-coloring, is, 5-edge-coloring such all are normal. this paper, we prove result related to conjecture. parameter μ3 measurement for graphs, introduced Steffen in 2015. Our shows G at least |E(G)|−μ3(G) (which no less than 2735|E(G)|) This improves on some earlier results Bílková and Šámal.