Repozytorium publikacji - Politechnika Gdańska

Abstract: 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).

Autorzy

• dr inż. Magdalena Lemańska link otwiera się w nowej karcie ,
• dr inż. Magda Dettlaff link otwiera się w nowej karcie ,
• Jerzy Topp