On an annihilation number conjecture

Vadim E. Levit, Eugen Mandrescu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let α(G) denote the cardinality of a maximum independent set, while µ(G) be the size of a maximum matching in the graph G = (V, E). If α(G) + µ(G) = |V |, then G is a König-Egerváry graph. If d1 ≤ d2 ≤ · · · ≤ dn is the degree sequence of G, then the annihilation number a (G) of G is the largest integer k such that Pki=1 di ≤ |E|. A set A ⊆ V satisfying PvA deg(v) ≤ |E| is an annihilation set; if, in addition, deg (x) + PvA deg(v) > |E|, for every vertex x ∈ V (G) − A, then A is a maximal annihilation set in G. In 2011, Larson and Pepper conjectured that the following assertions are equivalent: (i) α (G) = a (G); (ii) G is a König-Egerváry graph and every maximum independent set is a maximal annihilating set. It turns out that the implication “(i) =≻ (ii)” is correct. In this paper, we show that the opposite direction is not valid, by providing a series of generic counterexamples.

Original languageEnglish
Pages (from-to)359-369
Number of pages11
JournalArs Mathematica Contemporanea
Issue number2
StatePublished - 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
cb This work is licensed under https://creativecommons.org/licenses/by/4.0/


  • Annihilation number
  • Annihilation set
  • König-Egerváry graph
  • Maximum independent set
  • Maximum matching


Dive into the research topics of 'On an annihilation number conjecture'. Together they form a unique fingerprint.

Cite this