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Independent Italian bondage of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 8، شماره 4، اسفند 2023، صفحه 649-664 اصل مقاله (471.02 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28662.1657 | ||
| نویسندگان | ||
| Saeed Kosari* 1؛ Jafar Amjadi* 2؛ Aysha Khan3؛ Lutz Volkmann4 | ||
| 1Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China | ||
| 2Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran | ||
| 3Department of Mathematics Prince Sattam bin Abdulaziz University Alkharj 11991, Saudi Arabia | ||
| 4Lehrstuhl II f{u}r Mathematik, RWTH Aachen University, 52056 Aachen, Germany | ||
| چکیده | ||
| An independent Italian dominating function (IID-function) on a graph $G$ is a function $f:V(G)\rightarrow\{0,1,2\}$ satisfying the conditions that (i) $\sum_{u\in N(v)}f(u)\geq2$ when $f(v)=0$, and (ii) the set of all vertices assigned non-zero values under $f$ is independent. The weight of an IID-function is the sum of its function values over all vertices, and the independent Italian domination number $i_{I}(G)$ of $G$ is the minimum weight of an IID-function on $G$. In this paper, we initiate the study of the independent Italian bondage number $b_{iI}(G)$ of a graph $G$ having at least one component of order at least three, defined as the smallest size of a set of edges of $G$ whose removal from $G$ increases $i_{I}(G)$. We show that the decision problem associated with the independent Italian bondage problem is NP-hard for arbitrary graphs. Moreover, various upper bounds on $b_{iI}(G)$ are established as well as exact values on it for some special graphs. In particular, for trees $T$ of order at least three, it is shown that $b_{iI}(T)\leq2$. | ||
| کلیدواژه‌ها | ||
| Independent Italian dominating function؛ independent Italian domination number؛ independent Italian bondage number | ||
| مراجع | ||
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