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Isolation Number versus Domination Number of Trees
(MDPI, 2021-06)
[Abstract] If 𝐺 = (Vɢ,Eɢ) is a graph of order n, we call 𝑆 ⊆ Vɢ an isolating set if the graph induced by Vɢ − Nɢ[𝑆] contains no edges. The minimum cardinality of an isolating set of 𝐺 is called the isolation number of ...
Resolving Sets Tolerant to Failures in Three-Dimensional Grids
(Springer Nature, 2022)
[Abstract] An ordered set S of vertices of a graph G is a resolving set for 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 ...
The Auslander-Reiten quiver of the category of m−periodic complexes
(Elsevier, 2024-05)
[Abstract]: Let A be an additive k−category and C≡m(A) be the category of m−periodic
complexes. For any integer m > 1, we study conditions under which the compression
b
functor Fm : C (A) → C≡m(A) preserves or reflects ...
Graphs with isolation number equal to one third of the order
(Elsevier B.V., 2024-05)
[Absctract]: A set D of vertices of a graph G is isolating if the set of vertices not in D and with no
neighbor in D is independent. The isolation number of G, denoted by ι(G), is the minimum
cardinality of an isolating ...