Results 31 to 40 of about 1,294 (93)
Open Locating-Dominating Sets in Circulant Graphs
Discussiones Mathematicae Graph Theory, 2022 Location detection problems have been studied for a variety of applications including finding faults in multiprocessors, contaminants in public utilities, intruders in buildings and facilities, and for environmental monitoring using wireless sensor ...
Givens Robin M. +2 more
doaj +1 more source
On Independent Domination in Planar Cubic Graphs
Discussiones Mathematicae Graph Theory, 2019 A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S.
Abrishami Gholamreza +2 more
doaj +1 more source
Bounds on Watching and Watching Graph Products
Discussiones Mathematicae Graph Theory, 2022 A watchman’s walk for a graph G is a minimum-length closed dominating walk, and the length of such a walk is denoted (G). We introduce several lower bounds for such walks, and apply them to determine the length of watchman’s walks in several grids.
Dyer Danny, Howell Jared
doaj +1 more source
Improving the Efficiency of Fuzzy Graphs and Their Complements Using Some Influencing Parameters
Journal of Mathematics, Volume 2025, Issue 1, 2025.This study focuses on constructing optimal network structures for fuzzy graph (FG) products. In graph theory, the complement of a FG product is essential since it analyses alternate interactions between the vertices. Such a complement is used to represent situations in which specific connections are deliberately excluded, which helps to understand ...
A. Meenakshi +4 more
wiley +1 more source
On The Total Roman Domination in Trees
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by ...
Amjadi Jafar +2 more
doaj +1 more source
On Well-Covered Direct Products
Discussiones Mathematicae Graph Theory, 2022 A graph G is well-covered if all maximal independent sets of G have the same cardinality. In 1992 Topp and Volkmann investigated the structure of well-covered graphs that have nontrivial factorizations with respect to some of the standard graph products.
Kuenzel Kirsti, Rall Douglas F.
doaj +1 more source
A Study on Variants of Status Unequal Coloring in Graphs and Its Properties
Journal of Mathematics, Volume 2024, Issue 1, 2024.Let G∧ be a simple connected graph with vertex set ϑG∧ and edge set ξG∧. The status of a vertex p∈ϑG∧ is defined as ∑q≠pd(p, q). A subset P of ϑG∧ is called a status unequal dominating set (stu‐dominating set) of G∧; for every q∈ϑ−P, there exists p in P such that p and q are adjacent and st(p) ≠ st(q).
Parvathy Gnana Sambandam +4 more
wiley +1 more source
Bipartite graphs with close domination and k-domination numbers
Open Mathematics, 2020 Let kk be a positive integer and let GG be a graph with vertex set V(G)V(G). A subset D⊆V(G)D\subseteq V(G) is a kk-dominating set if every vertex outside DD is adjacent to at least kk vertices in DD. The kk-domination number γk(G){\gamma }_{k}(G) is the
Ekinci Gülnaz Boruzanlı +1 more
doaj +1 more source
Squares and difference sets in finite fields [PDF]
, 2013 For infinitely many primes p = 4k+1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Z p such that the difference set B−B contains only quadratic residues. Namely, instead of the ”trivial” bound |B| ≤ √p we prove |B √p
Bachoc, C. +2 more
core
Maximal Independent Sets In Graphs With At Most r Cycles
, 2005 We find the maximum number of maximal independent sets in two families of graphs: all graphs with $n$ vertices and at most $r$ cycles, and all such graphs that are also connected.
Diestel +9 more
core +5 more sources