http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
ON THE DOMINATION NUMBER OF A GRAPH AND ITS SQUARE GRAPH
Murugan, E.,Joseph, J. Paulraj The Kangwon-Kyungki Mathematical Society 2022 한국수학논문집 Vol.30 No.2
For a given graph G = (V, E), a dominating set is a subset V' of the vertex set V so that each vertex in V \ V' is adjacent to a vertex in V'. The minimum cardinality of a dominating set of G is called the domination number of G and is denoted by γ(G). For an integer k ≥ 1, the k-th power G<sup>k</sup> of a graph G with V (G<sup>k</sup>) = V (G) for which uv ∈ E(G<sup>k</sup>) if and only if 1 ≤ d<sub>G</sub>(u, v) ≤ k. Note that G<sup>2</sup> is the square graph of a graph G. In this paper, we obtain some tight bounds for the sum of the domination numbers of a graph and its square graph in terms of the order, order and size, and maximum degree of the graph G. Also, we characterize such extremal graphs.
NORDHAUS-GADDUM TYPE RESULTS FOR CONNECTED DOMINATION NUMBER OF GRAPHS
E. Murugan,J. Paulraj Joseph The Kangwon-Kyungki Mathematical Society 2023 한국수학논문집 Vol.31 No.4
Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. A dominating set S is called a connected dominating set if the subgraph induced by S is connected. The minimum cardinality taken over all connected dominating sets of G is called the connected domination number of G, and is denoted by γ<sub>c</sub>(G). In this paper, we investigate the Nordhaus-Gaddum type results for the connected domination number and its derived graphs like line graph, subdivision graph, power graph, block graph and total graph, and characterize the extremal graphs.