TY - JOUR
T1 - 2-(Ddge-)Connected Edge Domination Number and Matching Number
AU - Li, Hengzhe
AU - Wei, Ankang
AU - Zhang, Shenggui
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature.
PY - 2023/4
Y1 - 2023/4
N2 - A k-connected (resp. k-edge-connected) edge dominating set D of a connected graph G is a subset of E(G) such that G[D] is k-connected (resp. k-edge-connected) and each e∈ E(G) \ D has at least one neighbor in D. The k-connected edge domination number (resp. k-edge-connected edge domination number) of a graph G is the minimum size of a k-connected (resp. k-edge-connected) edge dominating set of G, and denoted by γk(G) (resp. γk′(G)). In this paper, we investigate the relationship between matching number and 2-connected (resp. 2-edge-connected) edge domination number, and prove that for a graph G, if it is 2-edge-connected, then γ2′(G)≤5α′(G)-2, and if it is 2-connected, then γ2(G) ≤ 4 α′(G) - 1 , where α′(G) is the matching number of G.
AB - A k-connected (resp. k-edge-connected) edge dominating set D of a connected graph G is a subset of E(G) such that G[D] is k-connected (resp. k-edge-connected) and each e∈ E(G) \ D has at least one neighbor in D. The k-connected edge domination number (resp. k-edge-connected edge domination number) of a graph G is the minimum size of a k-connected (resp. k-edge-connected) edge dominating set of G, and denoted by γk(G) (resp. γk′(G)). In this paper, we investigate the relationship between matching number and 2-connected (resp. 2-edge-connected) edge domination number, and prove that for a graph G, if it is 2-edge-connected, then γ2′(G)≤5α′(G)-2, and if it is 2-connected, then γ2(G) ≤ 4 α′(G) - 1 , where α′(G) is the matching number of G.
KW - Connected edge dominating set
KW - Edge dominating set
KW - Maximal matching
UR - http://www.scopus.com/inward/record.url?scp=85150182681&partnerID=8YFLogxK
U2 - 10.1007/s00373-023-02626-y
DO - 10.1007/s00373-023-02626-y
M3 - 文章
AN - SCOPUS:85150182681
SN - 0911-0119
VL - 39
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
IS - 2
M1 - 31
ER -