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New results on upper domatic number of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 5، شماره 2، اسفند 2020، صفحه 125-137 اصل مقاله (394.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26719.1136 | ||
| نویسندگان | ||
| Libin Samuel* 1؛ MAYAMMA JOSEPH2 | ||
| 1CHRIST (Deemed to be University) | ||
| 2CHRIST(Deemed to be University) Hosur Road Bangalore-560029 | ||
| چکیده | ||
| For a graph $G = (V, E)$, a partition $\pi = \{V_1,$ $V_2,$ $\ldots,$ $V_k\}$ of the vertex set $V$ is an \textit{upper domatic partition} if $V_i$ dominates $V_j$ or $V_j$ dominates $V_i$ or both for every $V_i, V_j \in \pi$, whenever $i \neq j$. The upper domatic number $D(G)$ is the maximum order of an upper domatic partition of $G$. We study the properties of upper domatic number and propose an upper bound in terms of clique number. Further, we discuss the upper domatic number of certain graph classes including unicyclic graphs and power graphs of paths and cycles. | ||
| کلیدواژهها | ||
| Domination؛ Upper domatic partition؛ Upper domatic number؛ Transitivity | ||
| مراجع | ||
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1] E. J. Cockayne and S. T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977), no. 3, 247–261.
[2] F. Harary, Graph theory, Addison-Wesley Publishing Company, Inc, 1969.
[3] T. W. Haynes, J. T. Hedetniemi, S. T. Hedetniemi, and A. McRae, The transitivity of special graph classes, J. Combin. Math. Combin. Comput. (In press) (2017).
[4] T. W. Haynes, J. T. Hedetniemi, S. T. Hedetniemi, A. McRae, and N. Phillips, The upper domatic number of a graph, AKCE Int. J. Graphs Comb. (In press) (2018).
[5] J. T. Hedetniemi and S. T. Hedetniemi, The transitivity of a graph, J. Combin. Math. Combin. Comput. 104 (2018), 75–91. | ||
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