On L ( p , q )-labelling of planar graphs with girth five

A [Formula: see text]-[Formula: see text]-labelling of graph [Formula: see text] is a function [Formula: see text], and satisfy the following two requirements (1) if [Formula: see text], then [Formula: see text]; (2) if [Formula: see text] and [Formula: see text] are of distance two apart, then [Formula: see text], where [Formula: see text] and [Formula: see text] are integers with [Formula: see text]. There has been extensive research on [Formula: see text]-labelling of graphs. Let [Formula: see text] be a planar graph with maximum degree [Formula: see text], and [Formula: see text]. We prove that [Formula: see text], which improves the bound given by Dong[3].