Results 31 to 40 of about 259 (109)
Maximal Independent Sets In Graphs With At Most r Cycles
, 2005 Key Words: cycle, ear decomposition, maximal independent set AMS classification: Primary 05C35; Secondary 05C38, 05C69. We find the maximum number of maximal independent sets in two families of graphs.
Vincent R. Vatter +11 more
core +1 more source
Some Results on the Independence Polynomial of Unicyclic Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x)=∑k=0ns(G,k)xk$I(G,x) = \sum\nolimits_{k = 0}^n {s\left({G,k} \right)x^k }$, where s(
Oboudi Mohammad Reza
doaj +1 more source
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
Partitioning the vertices of a graph into two total dominating sets
, 2016 A total dominating set in a graph G is a set S of vertices of G such that every vertex in G is adjacent to a vertex of S. We study graphs whose vertex set can be partitioned into two total dominating sets.
Haynes, Teresa W. +2 more
core +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
Exact Dominion of the Prism Graph: Enumeration by Congruence Class via Cyclic Words
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.Let Gn = Cn□P2 be the prism graph on 2n vertices. The dominion ζ(Gn) counts the minimum dominating sets of Gn. Encoding column selections as cyclic words over a quaternary alphabet converts domination into explicit local adjacency constraints, reducing the count of minimum dominating sets to the enumeration of minimum‐weight admissible words.
Julian Allagan +4 more
wiley +1 more source
On the Lovasz O-number of Almost Regular Graphs With Application to Erdos-Renyi Graphs [PDF]
, 2006 AMS classifications: 05C69; 90C35 ...
Sotirov, R.; id_orcid +5 more
core +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