On the D-differential of a graph
AbstractLet [Formula: see text] be a graph of order n(G). For a subset S of V(G), the boundary of S is defined as [Formula: see text] where N(S) is the open neighborhood of S. The external private neighborhood set of v with respect to S is defined as [Formula: see text] For a subset S of V(G), the D...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2022-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2022.2147039 |
| Summary: | AbstractLet [Formula: see text] be a graph of order n(G). For a subset S of V(G), the boundary of S is defined as [Formula: see text] where N(S) is the open neighborhood of S. The external private neighborhood set of v with respect to S is defined as [Formula: see text] For a subset S of V(G), the D-differential of S is defined as [Formula: see text] where [Formula: see text] In this paper, we introduce the concept of D-differential of a graph G, which is defined as [Formula: see text] We present several lower and upper bounds of D-differential of a graph. We construct a Gallai-type theorem for the D-differential [Formula: see text] and double Roman domination number [Formula: see text] which states that [Formula: see text] Thus, we can utilize a relation between D-differential and double Roman domination number. The concept of D-differential can be a framework to find double Roman domination number of graphs. Actually, we determine the double Roman domination number of middle graphs. |
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| ISSN: | 0972-8600 2543-3474 |