Affiliation:
1. School of Mathematics, Nanjing University of Aeronautics & Astronautics, Nanjing, Jiangsu, PR China
Abstract
The 2-domination number ?2(G) of a graph G is the minimum cardinality of a
set S ? V(G) such that every vertex from V(G)\S is adjacent to at least
two vertices in S. The annihilation number a(G) is the largest integer k
such that the sum of the first k terms of the non-decreasing degree sequence
of G is at most the number of its edges. It was conjectured that ?2(G) ?
a(G)+1 holds for every non-trivial connected graph G. The conjecture was
earlier confirmed for graphs of minimum degree 3, trees, block graphs and
some bipartite cacti. However, a class of cacti were found as counterexample
graphs recently by Yue et al. [9] to the above conjecture. In this paper, we
consider the above conjecture from the positive side and prove that this
conjecture holds for all unicyclic graphs.
Publisher
National Library of Serbia
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