Results 61 to 70 of about 16,468 (299)

Total domination dot-stable graphs [PDF]

, 2011
A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G.
Haynes, Teresa W., Teresa W. Haynes, Rickett, Stephanie A., Stephanie A. Rickett   +3 more
core   +1 more source

Some notes on the isolate domination in graphs

AKCE International Journal of Graphs and Combinatorics, 2017
A subset of vertices of a graph is a dominating set of if every vertex in has a neighbor in . The domination number is the minimum cardinality of a dominating set of . A dominating set is an isolate dominating set if the induced subgraph has at least one
Nader Jafari Rad
doaj   +1 more source

Lower Bounds for the Total Distance $k$-Domination Number of a Graph

Theory and Applications of Graphs
For $k \geq 1$ and a graph $G$ without isolated vertices, a \emph{total distance $k$-dominating set} of $G$ is a set of vertices $S \subseteq V(G)$ such that every vertex in $G$ is within distance $k$ to some vertex of $S$ other than itself.
Randy R. Davila
doaj   +1 more source

Total restrained reinforcement in graphs

AKCE International Journal of Graphs and Combinatorics, 2016
In this paper we initiate the study of total restrained reinforcement in graphs. The total restrained reinforcement number in a graph G with no isolated vertex, is the minimum number of edges that have to be added to G so that the resulting graph has ...
Nader Jafari Rad, Lutz Volkmann
doaj   +1 more source

Guidelines for Pediatric Radiotherapy Simulation: A Report From the Children's Oncology Group Radiation Oncology Discipline

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Pediatric radiation therapy presents unique challenges compared to adult treatments, including those of immobilization, potential need for sedation, and the critical importance of accurate, reproducible positioning. Additionally, heightened attention to imaging doses is necessary to minimize long‐term toxicity in survivors.
Parham Alaei, Stephen Mihalcik, Sujith Baliga, Young Kwok, Dana Casey, Eric Ehler, Christiane Burton, John C. Breneman, Daphne A. Haas‐Kogan, Suzanne L. Wolden, Arnold C. Paulino, Nadia N. Laack, Natia Esiashvili, Sarah Milgrom, Christine Hill‐Kayser, Thomas J. Fitzgerald, John A. Kalapurakal, Chia‐Ho Hua   +17 more
wiley   +1 more source

Total domination excellent trees [PDF]

, 2003
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S (other than itself). The graph G is called total domination excellent if every vertex belongs to some total dominating set of G of ...
Henning, Michael A.
core   +1 more source

Total and paired domination stability in prisms [PDF]

, 2023
A set $D$ of vertices in an isolate-free graph is a total dominating set if every vertex is adjacent to a vertex in $D$. If the set $D$ has the additional property that the subgraph induced by $D$ contains a perfect matching, then $D$ is a paired ...
Michael A. Henning, Tumidajewicz, Elżbieta, Monika Pilśniak, Elżbieta Tumidajewicz, Pilśniak, Monika, Gorzkowska, Aleksandra, Aleksandra Gorzkowska, Henning, Michael A.   +7 more
core   +1 more source

Bounds On The Disjunctive Total Domination Number Of A Tree

Discussiones Mathematicae Graph Theory, 2016
Let G be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, γt(G).
Henning Michael A., Naicker Viroshan
doaj   +1 more source

The Role of “Adult‐Onset” Cancer Predisposition Genes in Pediatric Cancer: A Comprehensive Review

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Current literature estimates that 10% of pediatric cancers are caused by pathogenic or likely pathogenic (P/LP) germline variants in cancer predisposition genes (CPGs). Variants in CPGs thought to increase cancer risk exclusively during adulthood are referred to as “adult‐onset” CPGs (aoCPGs).
Maria Rozo, Miriam A. Bornhorst, Angela J. Waanders, Sara Zarnegar‐Lumley, Ashwin Lakshman Koppayi, Lucy A. Godley   +5 more
wiley   +1 more source

Two Short Proofs on Total Domination

Discussiones Mathematicae Graph Theory, 2013
A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set.
Bickle Allan
doaj   +1 more source