Results 11 to 20 of about 704 (29)

Alliance free and alliance cover sets

, 2008
A \emph{defensive} (\emph{offensive}) $k$-\emph{alliance} in $\Gamma=(V,E)$ is a set $S\subseteq V$ such that every $v$ in $S$ (in the boundary of $S$) has at least $k$ more neighbors in $S$ than it has in $V\setminus S$.
H. Fernau, I. G. Yero, I. G. Yero, Ismael Gonzalez Yero, J. A. Rodríguez, J. A. Rodríguez-Velázquez, J. M. Sigarreta, J. M. Sigarreta, José María Sigarreta, Juan Alberto Rodriguez-Velazquez, K. H. Shafique, K. H. Shafique, S. M. Hedetniemi, Sergio Bermudo   +13 more
core   +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, Sundareswaran Raman, Sakander Hayat, Swaminathan Venkatasubramanian, Xiaogang Liu   +4 more
wiley   +1 more source

A tight lower bound for the hardness of clutters

, 2017
A {\it clutter} (or {\it antichain} or {\it Sperner family}) $L$ is a pair $(V,E)$, where $V$ is a finite set and $E$ is a family of subsets of $V$ none of which is a subset of another.
Mkrtchyan, Vahan, Sargsyan, Hovhannes
core   +1 more source

A vizing-type theorem for matching forests [PDF]

, 2000
A well known Theorem of Vizing states that one can colour the edges of a graph by $\Delta +\alpha$ colours, such that edges of the same colour form a matching.
Keijsper, J.C.M.
core   +2 more sources

Star-factors of tournaments

, 1997
Let S_m denote the m-vertex simple digraph formed by m-1 edges with a common tail. Let f(m) denote the minimum n such that every n-vertex tournament has a spanning subgraph consisting of n/m disjoint copies of S_m. We prove that m lg m - m lg lg m
Chen, Guantao, Lu, Xiaoyun, West, Douglas B.   +2 more
core   +2 more sources

The Cartesian product of graphs with loops [PDF]

, 2014
We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi-Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at least one ...
Christiaan E. Van De Woestijne, Florian Lehner, Johannes Cuno, Technische Universität Graz, Technische Universität Graz, Technische Universität Graz, Tetiana Boiko, Wilfried Imrich   +7 more
core  

Eigenvalues and Perfect Matchings [PDF]

AMS classification: 05C50, 05C70, 05E30.graph;perfect matching;Laplacian matrix;eigenvalues.
Brouwer, A.E., Haemers, W.H.
core   +1 more source

Factor-Critical Property in 3-Dominating-Critical Graphs

, 2006
A vertex subset $S$ of a graph $G$ is a dominating set if every vertex of $G$ either belongs to $S$ or is adjacent to a vertex of $S$. The cardinality of a smallest dominating set is called the dominating number of $G$ and is denoted by $\gamma(G)$.
Wang, Tao, Yu, Qinglin
core  

Some stable and closed-shell structures of anticancer drugs by graph theoretical parameters. [PDF]

Heliyon, 2023
Koam ANA, Ahmad A, Azeem M, Hakami KH, Elahi K.   +4 more
europepmc   +1 more source

Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application. [PDF]

Int J Appl Comput Math, 2022
Nazeer I, Rashid T.
europepmc   +1 more source