Results 41 to 50 of about 437 (67)

An Upper Bound on the Total Roman { 2 } -domination Number of Graphs with Minimum Degree Two

Journal of Combinatorial Mathematics and Combinatorial Computing
A total Roman \(\{2\}\)-dominating function on a graph \(G = (V,E)\) is a function \(f:V\rightarrow\{0,1,2\}\) with the properties that (i) for every vertex \({v}\in V\) with \(f({v})=0\), \(f(N({v}))\ge2\) and (ii) the set of vertices with \(f({v})>0 ...
M. Kheibari, H. Ahangar, R. Khoeilar, S. M. Sheikholeslami   +3 more
semanticscholar   +1 more source

Improved Total Domination and Total Roman Domination in Unit Disk Graphs

arXiv.org
Let $G=(V, E)$ be a simple undirected graph with no isolated vertex. A set $D_t\subseteq V$ is a total dominating set of $G$ if $(i)$ $D_t$ is a dominating set, and $(ii)$ the set $D_t$ induces a subgraph with no isolated vertex. The total dominating set
Sasmita Rout, G. K. Das
semanticscholar   +1 more source

On the Complexity of Signed Roman Domination

arXiv.org
Given a graph $G = (V, E)$, a signed Roman dominating function is a function $f: V \rightarrow \{-1, 1, 2\}$ such that for every vertex $u \in V$: $\sum_{v \in N[u]} f(v) \geq 1$ and for every vertex $u \in V$ with $f(u) = -1$, there exists a vertex $v ...
Sangam Balchandar Reddy
semanticscholar   +1 more source

Trees with total Roman domination number equal to Roman domination number plus its domination number: complexity and structural properties

AKCE International Journal of Graphs and Combinatorics, 2022
H. Abdollahzadeh Ahangar
semanticscholar   +2 more sources

Nonnegative signed total Roman domination in graphs

, 2020
N. Dehgardi, L. Volkmann
semanticscholar   +1 more source

Signed total Italian k-domination in graphs

, 2021
L. Volkmann
semanticscholar   +1 more source

Bounds on signed total double Roman domination

, 2020
L. Shahbazi, H. Ahangar, R. Khoeilar, S. Sheikholeslami   +3 more
semanticscholar   +1 more source

New bounds on the outer-independent total double Roman domination number

Discret. Math. Algorithms Appl., 2023
S. Sheikholeslami, L. Volkmann
semanticscholar   +1 more source

Signed Total Roman Dominating Functions of Corona Product of a Path with a Complete Graph

, 2017
C. Rani, S. Begum, G. Raju, S. Mohiddin
semanticscholar   +1 more source

Further Progress on the Total Roman $$\{2\}$$ { 2 } -Domination Number of Graphs

Bulletin of the Iranian Mathematical Society, 2021
H. Abdollahzadeh Ahangar, M. Chellali, M. Hajjari, S. Sheikholeslami   +3 more
semanticscholar   +1 more source