Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Iztok Peterin"'
Publikováno v:
AIMS Mathematics, Vol 6, Iss 10, Pp 11084-11096 (2021)
Let $ G $ be a graph with vertex set $ V(G) $. A function $ f:V(G)\rightarrow \{0, 1, 2\} $ is a Roman dominating function on $ G $ if every vertex $ v\in V(G) $ for which $ f(v) = 0 $ is adjacent to at least one vertex $ u\in V(G) $ such that $ f(u)
Externí odkaz:
https://doaj.org/article/57419cd95dd74d7f84f4eabe98d4a234
Publikováno v:
Opuscula Mathematica, Vol 40, Iss 3, Pp 375-382 (2020)
A subset \(D\) of the vertex set \(V\) of a graph \(G\) is called an \([1,k]\)-dominating set if every vertex from \(V-D\) is adjacent to at least one vertex and at most \(k\) vertices of \(D\). A \([1,k]\)-dominating set with the minimum number of v
Externí odkaz:
https://doaj.org/article/96b425d77316409785197ebc4479a1a7
Autor:
Iztok Peterin
Publikováno v:
Opuscula Mathematica, Vol 39, Iss 3, Pp 425-431 (2019)
Let \(G\) be a graph with vertex set \(V(G)\), \(\delta(G)\) minimum degree of \(G\) and \(k\in\left\{1-\left\lceil\frac{\delta(G)}{2}\right\rceil,\ldots ,\left\lfloor \frac{\delta(G)}{2}\right\rfloor\right\}\). Given a nonempty set \(M\subseteq V(G)
Externí odkaz:
https://doaj.org/article/0a488fc4689c4ad8b6316a2333e43e5b
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol vol. 22 no. 4, Iss Graph Theory (2020)
The packing number of a graph $G$ is the maximum number of closed neighborhoods of vertices in $G$ with pairwise empty intersections. Similarly, the open packing number of $G$ is the maximum number of open neighborhoods in $G$ with pairwise empty int
Externí odkaz:
https://doaj.org/article/208b4f8fc3e64c54ad3bb4841add2435
Autor:
Iztok Peterin, Petra Žigert Pleteršek
Publikováno v:
Opuscula Mathematica, Vol 38, Iss 1, Pp 81-94 (2018)
The Wiener index of a connected graph \(G\) is the sum of distances between all pairs of vertices of \(G\). The strong product is one of the four most investigated graph products. In this paper the general formula for the Wiener index of the strong p
Externí odkaz:
https://doaj.org/article/e274b354f5624291b284eb70d52509cd
Autor:
Iztok Peterin, Gabriel Semanišin
Publikováno v:
Mathematics, Vol 9, Iss 14, p 1592 (2021)
A shortest path P of a graph G is maximal if P is not contained as a subpath in any other shortest path. A set S⊆V(G) is a maximal shortest paths cover if every maximal shortest path of G contains a vertex of S. The minimum cardinality of a maximal
Externí odkaz:
https://doaj.org/article/33646f681ee14968a922b1f7ba774cde
Publikováno v:
Mathematics, Vol 8, Iss 9, p 1438 (2020)
Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2} such that every vertex u with f(u)=0 is adjacent to a vertex v with f(v)=2, and the set of vertices with positive labels induces a graph
Externí odkaz:
https://doaj.org/article/460c5efa74d64c35b41ec6ba9ab10856
Autor:
Dragana Božović, Iztok Peterin
Publikováno v:
Mathematics, Vol 8, Iss 4, p 496 (2020)
A digraph D is an efficient open domination digraph if there exists a subset S of V ( D ) for which the open out-neighborhoods centered in the vertices of S form a partition of V ( D ) . In this work we deal with the efficient open domination digraph
Externí odkaz:
https://doaj.org/article/6cf7ae0f3f9e4b3e9a7ab789570e8d07
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol Vol. 18 no. 3, Iss Graph Theory (2016)
A graph is an efficient open domination graph if there exists a subset of vertices whose open neighborhoods partition its vertex set. We characterize those graphs $G$ for which the Cartesian product $G \Box H$ is an efficient open domination graph wh
Externí odkaz:
https://doaj.org/article/fb1b4606e5f84f24afe0532fdc8b8202
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol Vol. 18 no. 3, Iss Graph Theory (2016)
Closed monopolies in graphs have a quite long range of applications in several problems related to overcoming failures, since they frequently have some common approaches around the notion of majorities, for instance to consensus problems, diagnosis p
Externí odkaz:
https://doaj.org/article/6f8b1f3bf11b44f6bf2d32b32a5aebea