TWIN EDGE COLORING OF SOME PATH AND CYCLE RELATED GRAPHS | Asian Journal of Mathematics

A twin edge -coloring of a graph is a proper edge -coloring of with the elements of so that the induced vertex -coloring is a proper vertex -coloring, in which the colour of a vertex in is the sum in of the colours of the edges incident with. The twin chromatic index of is the least for which has a twin edge k- colouring. The splitting graph of path and cycle, middle graph of path and cycle, and shadow graph of path and cycle all have twin chromatic indexes. The twin chromatic index of is likewise calculated, where denotes the direct product of and and are the cycle and path on r vertices, respectively.

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