Independent domination number in Cayley digraphs of rectangular groups

Nupo, Nuttawoot; Panma, Sayan

doi:10.1142/s1793830918500246

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Furthermore, Bacolod and Baldado Jr. [2] created another new binary operation on graphs in 2014, called acquaint vertex gluing and focused on its domination number. As same as the work of Nupo and Panma [11], they investigated the domination number of Cayley digraphs of rectangular groups.…”

Section: Introductionmentioning

confidence: 97%

The Domination Number of a Graph $P_k((k_1,k_2),(k_3,k_4))$

Ruangnai

Panma

2019

Comm. Math. & Appl.

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For each k, k 1 , k 2 , k 3 , k 4 ∈ N, we will denote by P k (k 1 , k 2), (k 3 , k 4) a tree of k + k 1 + k 2 + k 3 + k 4 + 1 vertices with the degree sequence (1, 1, 1, 1, 2, 2, 2,. .. , 2, 3, 3). Let α k 1 , β k 2 , σ k 3 , and δ k 4 be all four endpoints of the graph. Let the distance between both vertices of degree 3 be equal to k. A subset S of vertices of a graph P k (k 1 , k 2), (k 3 , k 4) is a dominating set of P k (k 1 , k 2), (k 3 , k 4) if every vertex in V P k (k 1 , k 2), (k 3 , k 4) − S is adjacent to some vertex in S. We investigate the dominating set of minimum cardinality of a graph P k (k 1 , k 2), (k 3 , k 4) to obtain the domination number of this graph. Finally, we determine an upper bound on the domination number of a graph P k (k 1 , k 2), (k 3 , k 4) .

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Section: Introductionmentioning

confidence: 97%

The Domination Number of a Graph $P_k((k_1,k_2),(k_3,k_4))$

Ruangnai

Panma

2019

Comm. Math. & Appl.

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“…In 2018, Hao and Qian [10] introduced bounds on the domination number of a digraph. Moreover, Nupo and Panma [14] investigated the independent domination number in Cayley digraphs of rectangular groups. Recently, in 2019, Sivagami and Chelvam [17] considered the domination number of the trace graph of matrices.…”

Section: Introductionmentioning

confidence: 99%

Domination parameters on Cayley digraphs of transformation semigroups with fixed sets

Nupo¹,

Pookpienlert²

2021

Turk J Math

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For a nonempty subset Y of a nonempty set X , denote by F ix(X, Y ) the semigroup of full transformations on the set X in which all elements in Y are fixed. The Cayley digraph Cay(F ix(X, Y ), A) of F ix(X, Y ) with respect to a connection set A ⊆ F ix(X, Y ) is defined as a digraph whose vertex set is F ix(X, Y ) and two vertices α, β are adjacent in sense of drawing a directed edge (arc) from α to β if there exists µ ∈ A such that β = αµ . In this paper, we determine domination parameters of Cay(F ix(X, Y ), A) where A is a subset of F ix(X, Y ) related to minimal idempotents and permutations in F ix(X, Y ).

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γ-induced-paired dominating graphs of paths and cycles

Sanguanpong

Trakultraipruk

2022

Discrete Math. Algorithm. Appl.

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For any graph [Formula: see text], a nonempty subset [Formula: see text] of [Formula: see text] is called an induced-paired dominating set if every vertex in [Formula: see text] is adjacent to some vertex in [Formula: see text], and the induced subgraph [Formula: see text] contains only independent edges. An induced-paired dominating set of [Formula: see text] with minimum number of vertices is also called a [Formula: see text]-set. We define the [Formula: see text]-induced paired dominating graph of [Formula: see text], denoted by [Formula: see text], to be the graph whose vertex set consists of all [Formula: see text]-sets, and two [Formula: see text]-sets are adjacent in [Formula: see text] if they are different from each other by only one vertex. In this paper, we exhibit all [Formula: see text]-induced-paired dominating graphs of paths and cycles.

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Independent domination number in Cayley digraphs of rectangular groups

Cited by 3 publications

References 14 publications

The Domination Number of a Graph $P_k((k_1,k_2),(k_3,k_4))$

The Domination Number of a Graph $P_k((k_1,k_2),(k_3,k_4))$

Domination parameters on Cayley digraphs of transformation semigroups with fixed sets

γ-induced-paired dominating graphs of paths and cycles

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