A (1,2) – dominating set in a graph G = (V,E) is a set S having the property that for every vertex v in V – S there is atleast one vertex in S at distance 1 from v and a second vertex in S at distance atmost 2 from v.
We also determine bounds on the cardinality of minimum [1, 2]-sets, and investigate extremal graphs achieving these bounds. This study has implications for ...
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Oct 1, 2014 · A vertex subset of a graph is a -set if, for every vertex, that is, each vertex is adjacent to either one or two vertices in.
[1, 2]-sets in graphs ... We also determine bounds on the cardinality of minimum [1, 2]-sets, and investigate extremal graphs achieving these bounds.
A dominating set like D of graph G(V, E), called [1, 2]-dominating set, if each vertex v ∈ V \ D is adjacent to at most two vertices in D.
In this paper, we give some sharp bounds for the $k$-tuple total restrained domination number of a graph, and also calculate it for some of the known ...
Sep 26, 2018 · A subset in a graph is a connected [j, k]-set, if it satisfies that G[S] is a connected subgraph of G and every vertex , for non-negative ...
A subset S ⊆ V in a graph G = (V,E) is a total [1, 2]-set if, for every vertex $$ \upsilon \in V, 1 \leq\mid N (\upsilon)\cap S\mid\leq $$υ∈V,1≤∣N(υ)∩S∣≤.
Mar 7, 2024 · In this paper, we propose a polynomial-time algorithm for computing a minimum [1,2]-dominating set on interval graphs by a dynamic programming technique.
A [1,2] - dominating set S of a graph G = (V,E) is an accurate [1,2]− dominating set, if V − S has no [1,2] - dominating set of cardinality |S|. The accurate [1 ...