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Papers by Jenq-Jong Lin

Applied Mathematical Sciences

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Applied Mathematical Sciences

This article is distributed under the Creative Commons by-nc-nd Attribution License.

Applied Mathematical Sciences, 2020

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International Journal of Contemporary Mathematical Sciences, 2018

An independent set is a set of vertices in a graph, no two of which are adjacent. A maximal indep... more An independent set is a set of vertices in a graph, no two of which are adjacent. A maximal independent set is an independent set that is not a proper subset of any other independent set. Note that in general counting the number of maximal independent sets in a graph is NP-complete [5]. In this paper, we give two linear-time algorithms to characterize all the maximal independent sets of the path P n and the cycle C n .

Applied Mathematical Sciences, 2021

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Proceedings of the 2017 International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2017), 2017

A set S of vertices is a dominating set of G if NG[S]=V(G). The domination number γ(G) of a graph... more A set S of vertices is a dominating set of G if NG[S]=V(G). The domination number γ(G) of a graph G is the minimum cardinality among all dominating sets of G. The decision problem of determining the domination number for arbitrary graphs is NP-complete. Here we focus on trees. If x and x' are duplicated leaves adjacent to the same support vertex in a tree T, then γ(Tx')= γ(T). If T' can be obtained from T by adding some duplicated leaves, we can see that γ(T')= γ(T). So the maximum order of a tree T, which is γ(T)=k, is infinity. In this paper, we focus on trees which are without duplicated leaves. For k≧1, we determine the minimum and maximum orders of the trees T which are without duplicated leaves and γ(T)=k. Moreover, we characterize the trees of minimum and maximum orders.

The International Journal of Contemporary Mathematical Sciences, 2017

A cactus graph is a connected graph in which any two cycles have at most one vertex in common. Le... more A cactus graph is a connected graph in which any two cycles have at most one vertex in common. Let γ(G) and γc(G) be the domination number and connected domination number of a graph G, respectively. We can see that γ(G) ≤ γc(G) for any graph G. S. Arumugam and J. Paulraj Joseph [1] have characterized trees, unicyclic graphs and cubic graphs with equal domination and connected domination numbers. A few years later, Xue-gang Chena, Liang Suna, Hua-ming Xing [3] characterized the cactus graphs for which the domination number is equal to the connected domination number. Their characterization is in terms of global properties of a construction. In this paper, we provide a constructive characterization of the cactus graphs with equal domination and connected domination numbers. Mathematics Subject Classification: 05C69

The distance between two vertices u and v in a graph equals the length of a shortest path from u ... more The distance between two vertices u and v in a graph equals the length of a shortest path from u to v. The distance-2 domination number of a graph G, denoted by γ2(G), is the minimum cardinality of a vertex subset where every vertex not belonging to the set is within distance two from some element of the set. The independent domination number of a graph G, denoted by γi(G), is the minimum cardinality of a vertex subset that it is an independent set and every vertex not belonging to the set is adjacent to an element of the set. A weak-tree is a tree which has no duplicated leaf. Here we focus on the weak-trees. Let T (n) be the set of weak-trees T̃ satisfying γ2(T̃ ) = γi(T̃ ) = n. In this paper, we provide a constructive characterization of T (n) for all n ≥ 2. Mathematics Subject Classification: 05C05, 05C69

The International Journal of Contemporary Mathematical Sciences, 2021

The distance between two vertices u and v in a graph equals the length of a shortest path from u ... more The distance between two vertices u and v in a graph equals the length of a shortest path from u to v. The distance-2 domination number of a graph G, denoted by γ2(G), is the minimum cardinality of a vertex subset where every vertex not belonging to the set is within distance two from some element of the set. The total domination number of a graph G, denoted by γt(G), is the minimum cardinality of a vertex subset where every vertex of G is adjacent to an element of the set. For any nontrivial connected graph G, we can see that γt(G) ≥ 2. Here we focus on the trees. For n ≥ 1, let T (n) be the set of trees T satisfying γt(T ) = 2γ2(T ) = 2n. In this paper, we provide a constructive characterization of T (n) for all n ≥ 1. Mathematics Subject Classification: 05C05, 05C69

International Journal of Contemporary Mathematical Sciences, 2020

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International Journal of Contemporary Mathematical Sciences, 2020

This article is distributed under the Creative Commons by-nc-nd Attribution License.

International Journal of Contemporary Mathematical Sciences, 2020

This article is distributed under the Creative Commons by-nc-nd Attribution License.

Open Journal of Discrete Mathematics, 2016

Let 2 0 mod λ .

DEStech Transactions on Computer Science and Engineering, 2020

A maximal independent set is an independent set that is not a proper subset of any other independ... more A maximal independent set is an independent set that is not a proper subset of any other independent set. Given a graph G of order n, we define the m P-extended of G, denoted G(m), as the graph consisting of G together with n copies of m P , a leaf of each path attached to exactly one vertex of G. In this paper, we determine the number of maximal independent sets of the m P-extended of a star and a path.

DEStech Transactions on Computer Science and Engineering, 2020

International Journal of Contemporary Mathematical Sciences, 2018

Let L = {H 1 , H 2 ,. .. , H r } be a family of subgraphs of a graph G. An L-decomposition of G i... more Let L = {H 1 , H 2 ,. .. , H r } be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer α i copies of H i , where i ∈ {1, 2,. .. , r}. Let S(C k/2) and S k denote a sun and a star with k edges, respectively. In this paper, we prove that a balanced complete bipartite graph with 2n vertices has a {S(C k/2), S k }-decomposition if and only if 8 ≤ k ≤ n, k ≡ 0 (mod 4) and n 2 ≡ 0 (mod k).

International Journal of Contemporary Mathematical Sciences, 2019

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International Journal of Contemporary Mathematical Sciences, 2018

The distance between two vertices u and v in a graph G equals the length of a shortest path from ... more The distance between two vertices u and v in a graph G equals the length of a shortest path from u to v. A set I of vertices is distance-k independent if every vertex in I is at distance at least k + 1 to any other vertex of I. A set I of vertices is distance-k dominating if every vertex not belonging to I is at distance at most k of a vertex in I. A set of vertices is a distance-k independent dominating set if and only if this set is a distance-k independent set and a distance-k dominating set. Note that in general counting the number of independent dominating sets in a graph is NP-complete [2]. In this paper, we want to characterize all the distance-k independent dominating sets of the path P n. Besides, we calculate the number of the distance-k independent dominating sets of P n .

Open Journal of Discrete Mathematics, 2017

A maximal independent set is an independent set that is not a proper subset of any other independ... more A maximal independent set is an independent set that is not a proper subset of any other independent set. A connected graph (respectively, graph) G with vertex set () V G is called a quasi-tree graph (respectively, quasi-forest graph), if there exists a vertex () x V G ∈ such that G x − is a tree (respectively, forest). In this paper, we survey on the large numbers of maximal independent sets among all trees, forests, quasi-trees and quasi-forests. In addition, we further look into the problem of determining the third largest number of maximal independent sets among all quasi-trees and quasi-forests. Extremal graphs achieving these values are also given.

International Journal of Contemporary Mathematical Sciences, 2017

In this paper we complete the determination of the k-th (3 ≤ k ≤ n−1 2) largest numbers of maxima... more In this paper we complete the determination of the k-th (3 ≤ k ≤ n−1 2) largest numbers of maximal independent sets among all quasiforest graphs of order n ≥ 8 and characterize the extremal graphs.