15 research outputs found
Bondage number of grid graphs
The bondage number of a nonempty graph is the cardinality of a
smallest set of edges whose removal from results in a graph with domination
number greater than the domination number of . Here we study the bondage
number of some grid-like graphs. In this sense, we obtain some bounds or exact
values of the bondage number of some strong product and direct product of two
paths.Comment: 13 pages. Discrete Applied Mathematics, 201
Common Independence in Graphs
The cardinality of a largest independent set of G, denoted by α(G), is called the independence number of G. The independent domination number i(G) of a graph G is the cardinality of a smallest independent dominating set of G. We introduce the concept of the common independence number of a graph G, denoted by αc(G), as the greatest integer r such that every vertex of G belongs to some independent subset X of VG with |X|≥r. The common independence number αc(G) of G is the limit of symmetry in G with respect to the fact that each vertex of G belongs to an independent set of cardinality αc(G) in G, and there are vertices in G that do not belong to any larger independent set in G. For any graph G, the relations between above parameters are given by the chain of inequalities i(G)≤αc(G)≤α(G). In this paper, we characterize the trees T for which i(T)=αc(T), and the block graphs G for which αc(G)=α(G)