Weak Roman Domination In 4*n Grid Graph

In order to study the problem of weak Roman dominatian in a m×n grid graph, westart from a m×n grid graph with m 6 4 and make search at every step thorough. Wecan receive the following information from the cultural heritage:Based on an article by Ian Stewart"Denfend the Roman Empire!", Roman dominatingfunction( RDF) is presented. M. A. Henning use a new strategy to defend the RomanEmpire, the strategy save costs, while it can also defend the Roman Empire. Which isWeak Roman dominating function( WRDF). The bonding of grid graph and weak Romandomination provides new space for the search of weak Rome domination, the weak Romandomination number of a 2×n or 3×n grid graph is already determined.In this paper, we use new method to study 4×n grid graph and determine the weakRoman domination number of 4×n grid graph and provide verification process.