A complete partition of a graph G = (V, E) is a partition of the vertex set V in which there is a... more A complete partition of a graph G = (V, E) is a partition of the vertex set V in which there is an edge connecting every pair of distinct classes. That is, a partition V 1 ,…,V t of V is complete if, for every i, j, i ≠ j, there is an edge {v i , v j } such that v i ∈ V i and v j ∈ V j. In this paper we study the problem of finding a complete partition of the largest possible size for certain finite, simple and undirected graphs. This concept is interpreted in terms of graph vertex colorings. In the process we give (1)illustrations, (2)prove results, (3)indicate the scope of its application and also raise some open problems.
International Journal of Mathematical Analysis, 2015
The concept of vertex coloring pose a number of challenging open problems in graph theory. Among ... more The concept of vertex coloring pose a number of challenging open problems in graph theory. Among several interesting parameters, the coloring parameter, namely the pseudoachromatic number of a graph stands a class apart. Although not studied very widely like other parameters in the graph coloring literature, it has started gaining prominence in recent years. The pseudoachromatic number of a simple graph G, denoted ψ(G), is the maximum number of colors used in a vertex coloring of G, where the adjacent vertices may or may not receive the same color but any two distinct pair of colors are represented by at least one edge in it. In this paper we have computed this parameter for a number of classes of graphs.
International Journal of Pure and Apllied Mathematics, 2015
In this paper, we determine for a simple graph G on n vertices and m edges a variety of dominatio... more In this paper, we determine for a simple graph G on n vertices and m edges a variety of domination parameters such as connected domination number, outer connected domination number, doubly connected domination number, global domination number, total global connected domination number, 2-connected domination number, strong domination number, fair domination number, independence domination number etc.
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Papers by B Logeshwary