منابع مشابه
Adjacency metric dimension of the 2-absorbing ideals graph
Let Γ=(V,E) be a graph and W_(a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),… ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...
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15 صفحه اولThe metric dimension and girth of graphs
A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
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A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let Gβ,D be the set of graphs with metric dimension β and diameter D. It is well-known that the minimum order of a graph in Gβ,D is exactly β + D. The first contribution of this pape...
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A set of vertices S resolves a graph if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of a graph is the minimum cardinality of a resolving set of the graph. Fix a connected graph G on q ≥ 2 vertices, and let M be the distance matrix of G. We prove that if there exists w ∈ Z such that ∑ i wi = 0 and the vector Mw, after sorting its coor...
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ژورنال
عنوان ژورنال: Journal of the Indonesian Mathematical Society
سال: 2019
ISSN: 2460-0245,2086-8952
DOI: 10.22342/jims.25.1.747.75-84