Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Outer independent total double Italian domination number
Authors: Seyed Mahmoud Sheikholeslami, Lutz Volkmann
Keywords: double Italian domination. Outer independent (total) double Italian domination.
– 0.28 Mb
Keywords: double Italian domination. Outer independent (total) double Italian domination.
Abstract
If $G$ is a graph with vertex set $V(G)$, then let $N[u]$ be the closed neighborhood of the vertex $u\in V(G)$. A total double Italian dominating function (TDIDF) on a graph $G$ is a function $f:V(G)\rightarrow\{0,1,2,3\}$ satisfying (i) $f(N[u])\ge 3$ for every vertex $u\in V(G)$ with $f(u)\in\{0,1\}$ and (ii) the subgraph induced by the vertices with a non-zero label has no isolated vertices. A TDIDF is an outer-independent total double Italian dominating function (OITDIDF) on $G$ if the set of vertices labeled $0$ induces an edgeless subgraph. The weight of an OITDIDF is the sum of its function values over all vertices, and the outer independent total double Italian domination number $\gamma_{tdI}^{oi}(G)$ is the minimum weight of an OITDIDF on $G$. In this paper, we establish various bounds on $\gamma_{tdI}^{oi}(G)$, and we determine this parameter for some special classes of graphs.Seyed Mahmoud Sheikholeslami
ORCID: https://orcid.org/0000-0003-2298-4744
Department of Mathematics
Azarbaijan Shahid Madani University
Tabriz, I. R. Iran
E-mail:
Lutz Volkmann
ORCID: https://orcid.org/0000-0003-3496-277X
Lehrstuhl C für Mathematik
RWTH Aachen University
52062 Aachen, Germany
E-mail:
ORCID: https://orcid.org/0000-0003-2298-4744
Department of Mathematics
Azarbaijan Shahid Madani University
Tabriz, I. R. Iran
E-mail:
Lutz Volkmann
ORCID: https://orcid.org/0000-0003-3496-277X
Lehrstuhl C für Mathematik
RWTH Aachen University
52062 Aachen, Germany
E-mail:
DOI
https://doi.org/10.56415/csjm.v32.02Fulltext
– 0.28 Mb
Contents
- Formal Analysis of Medical Systems using Multi-Agent Systems with Information Sharing
- Outer independent total double Italian domination number
- On the trees with maximum Cardinality-Redundance number
- Vector finite fields of characteristic two as algebraic support of multivariate cryptography
- Optimizing Cervical Cancer Classification with SVM and Improved Genetic Algorithm on Pap Smear Images
- A Binary Grey Wolf Optimizer with Mutation for Mining Association Rules
- A Coloured Petri Net-based approach and Genetic Algorithms for improving services in the Emergency Department
- Efficient GPU Power Management through Advanced Framework Utilizing Optimization Algorithms
