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Roman domination signed roman domination and Cartesian product of graphs

 Department:Mathematics and Statistics  
 By:usericon Misa_Percy1  

 Project ID: 8068
 Rating:  (5.0) votes: 1
   Price:₦4000
Abstract
In this project, we continue the study of Roman dominating functions in graphs. A signed Roman dominating function (SRDF) on a graph G  (V, E) is a function f:V{-1, 1, 2} satisfying the conditions that (i) the sum of its function values over any closed neighborhood is at least one and (ii) for every vertex u for which f (u)-1 is adjacent to at least one vertex v for which f (v)  2. The weight of an SRDF is the sum of its function values over all vertices. The signed Roman domination number of G is the minimum weight of an SRDF in G. Problems on the Cartesian product are also solved and interesting theorems proved on topics of contemporary interest in graph theory. Here we survey recent developments on the structure of the Cartesian product with emphasis on paths and paths graphs....
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