Total domination number of central trees
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let $\gamma_{t}(G)$ and $\tau(G)$ denote the total domination number and vertex cover number of graph $G$, respectively. In this paper, we study the total domination number of the central tree $C(T)$ for a tree $T$. First, a relationship between the total domination number of $C(T)$ and the vertex cover number of tree $T$ is discussed. We characterize the central trees with equal total domination number and independence number. Applying the first result, we improve the upper bound on the total domination number of $C(T)$ and solve one open problem posed by Kazemnejad et al..
Abstract
Let $\gamma_{t}(G)$ and $\tau(G)$ denote the total domination number and vertex cover number of graph $G$, respectively. In this paper, we study the total domination number of the central tree $C(T)$ for a tree $T$. First, a relationship between the total domination number of $C(T)$ and the vertex cover number of tree $T$ is discussed. We characterize the central trees with equal total domination number and independence number. Applying the first result, we improve the upper bound on the total domination number of $C(T)$ and solve one open problem posed by Kazemnejad et al..
참고문헌 (6)
- E. J. Cockayne, "Total domination in graphs", Networks, 10(3), pp.211~219 (1980), Wiley[DOI]
- T. W. Haynes, "Fundamentals of domination in graphs" (1998), Marcel Dekker, Inc
- T. W. Haynes, "Domination in graphs" (1998), Marcel Dekker, Inc
- M. A. Henning, "Total domination in graphs, Springer Monographs in Mathematics" (2013), Springer
- Farshad Kazemnejad, "Total domination number of central graphs", 대한수학회보, 56(4), pp.1059~1075 (2019), 대한수학회[DOI]
- K. Thilagavathi, "Circumdetic graphs", Far East J. Appl. Math, 26(2), pp.191~201 (2007)