On upper bounds for the pseudo-achromatic index Original Research Article

In this paper, we give another approach to the pseudo-achromatic index and the achromatic index of a graph and study upper bounds for them. We have obtained the following best possible upper bounds: 1. (i) Ψ′(G) ⩽ Ψ′S(G) ⩽ ⦜(e(G) + χ′(G))/2; and 2. (ii) Ψ′(G) ⩽ Ψ′S(G) ⩽ max1 ⩽ k ⩽ ⦜p/2min⦜pΔ(G)/2k, 2k(Δ(G) − 1) + 1. Using these bounds, the pseudo-achromatic indices of graphs of certain types are obtained which generalize the results of Bouchet (1978), Chiang and Fu (1995), Geller and Kronk (1974) and Jamison (1989) for achromatic indices to pseudo-achromatic indices.