WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
The Complementary Join of a Graph
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Abstract: The complementary join of a graph G is introduced in this paper as the join $$G+\bar{G}$$ 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 $$G+\bar{G}$$ and determine when $$G+\bar{G}$$ 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 $$G+\bar{G}$$ 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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Keywords: Complementary join, Eulerian, L (2, 1)-labeling number, locating chromatic number, partition dimension
Pages: 147-153
DOI: 10.37394/23206.2024.23.17