Abstract
The complementary join of a graph G is introduced in this paper as the join G+G of G and its complement considering them as vertex-disjoint graphs. The aim of this paper is to study some properties and some graph invariants of the complementary join of a graph. We find the diameter, the radius and the domination number of G + G and determine when G + G is self-centered. We obtain a characterization of the Eulerian complementary joins, and show that the complementary join of a nontrivial graph is Hamiltonian. We give the clique and independence numbers of G + G in terms of the clique and independence numbers of G. We conclude this paper by determining the chromatic number, the L(2, 1)-labeling number, the locating chromatic number and the partition dimension of the complementary join of a star.
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