  Eternal vertex cover problem is a variant of the classical vertex cover
problem modeled as a two player attacker-defender game. Computing eternal
vertex cover number of graphs is known to be NP-hard in general and the
complexity status of the problem for bipartite graphs is open. There is a
quadratic complexity algorithm known for this problem for chordal graphs.
Maximal outerplanar graphs forms a subclass of chordal graphs, for which no
algorithm of sub-quadratic time complexity is known. In this paper, we obtain a
recursive algorithm of linear time for computing eternal vertex cover number of
maximal outerplanar graphs.
