Inverse Domination Number of Circulant Graph

Cynthia, V. Jude Annie; Kavitha, A.

doi:10.17654/dm023020075

Cited by 1 publication

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“…There are some graphs with equal domination and inverse domination numbers are identified by T.TamizhChelvam [2]. Inverse domination number of circulant graph proved by V.Cynthiya in [3]. Also we identified domination and inverse domination numbers for Wrapped butterfly network, Lollipop graph, Fly graph and Jellyfish graph in [19][20][21].…”

Section: Introductionmentioning

confidence: 72%

Inverse Domination in X-Trees and Sibling Trees

Shalini,

Rajasingh

2024

Eur. J. Pure Appl. Math.

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A set $D$ of vertices in a graph $G$ is a dominating set if every vertex not in $D$ is adjacent to at least one vertex in $D$. The minimum cardinality of a dominating set in $G$ is called the domination number and is denoted by $\gamma(G)$. Let $D$ be a minimum dominating set of $G$. If $V-D$ contains a dominating set say $D^{'}$ of $G$, then $D^{'}$ is called an inverse dominating set with respect to $D$. The inverse domination number $\gamma^{'}(G)$ is the cardinality of a minimum inverse dominating set of $G$. A dominating set $D$ is called a connected dominating set or an independent dominating set of $G$ according as the induced subgraph $\langle D \rangle$ is connected or independent in $G$. The minimum of the cardinalities of the connected dominating sets of $G$ or the independent dominating sets of $G$ is called the connected domination number $\gamma_{c} (G)$ or the independent domination number $\gamma_{i} (G)$ respectively. In this paper, we determine the inverse domination numbers in X-Trees and Sibling Trees. We have also determined the independent domination numbers of both the trees and the connected domination number of Sibling Trees. A result on inverse domination number of some classes of Hypertrees is also included.

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