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Let G = (V E) be a simple graph of order and be an integer with ≥ 1. The set X ⊆ V (G) is called an -packing if each two distinct vertices in X are more than apart. A packing colouring of G is a partition X = {X 1 X 2 X } of V (G) such that each colour class X is an -packing. The minimum order of a packing colouring is called the packing chromatic number of G, denoted by χ ρ (G). In this paper we show, using a theoretical proof, that if = 4 , for some integer ≥ 3, then 9 ≤ χ ρ (C 4 2C ) ≤ 11. We will also show that if is a multiple of four, then χ ρ (C 4 2C ) = 9.MSC: 05C69

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For positive integers ∆ and D we define n ∆,D to be the largest number of vertices in an outerplanar graph of given maximum degree ∆ and diameter D. We prove that n ∆

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