Vertex distinguishing colorings of graphs with Δ(G) = 2


In a paper by Burris and Schelp (J. Graph Theory 26 (2) (1997) 70), a conjecture was made concerning the number of colors χ′s(G) required to proper edge-color G so that each vertex has a distinct set of colors incident to it. We consider the case when Δ(G) = 2, so that G is a union of paths and cycles. In particular we find the exact values of χ′(G) and hence verify the conjecture when G consists of just paths or just cycles. We also give good bounds on χ′s(G) when G contains both paths and cycles. © 2002 by the American College of Cardiology.

Publication Title

Discrete Mathematics