Author
Min-Jen Jou
Bio: Min-Jen Jou is an academic researcher from National Chiao Tung University. The author has contributed to research in topics: Chordal graph & Maximal independent set. The author has an hindex of 5, co-authored 5 publications receiving 121 citations.
Papers
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TL;DR: In this article, the problem of determining the largest number of maximum independent sets of a graph of order n is studied, and solutions to this problem are given for various classes of graphs, including general graphs, trees, forests, (connected) graphs with at most one cycle, connected graphs and triangle-free graphs.
Abstract: In this paper, we study the problem of determining the largest number of maximum independent sets of a graph of order n. Solutions to this problem are given for various classes of graphs, including general graphs, trees, forests, (connected) graphs with at most one cycle, connected graphs and triangle-free graphs. Extremal graphs achieving the maximum values are also given.
51 citations
TL;DR: This paper determines the largest number of maximal independent sets among all connected graphs of order n, which contain at most one cycle, and characterize those extremal graphs achieving this maximum value.
31 citations
TL;DR: In this article, it was shown that every connected triangle, free graph of order n ⩾ 22 has at most 5 · 2 (n−6)/2 maximal independent sets if n is even (respectively, odd).
21 citations
Journal Article•
13 citations
TL;DR: The setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG ≅ K1) or duplicated vertices is studied and it is proved that |V(G)| ≤ 2k−1 +k − 2 for anyG inS(K) andk ≥ 2; consequently,S( k) is finite for anyk.
Abstract: Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG ? K 1) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| ≤ 2 k?1 +k ? 2 for anyG inS(k) andk ? 2; consequently,S(k) is finite for anyk.
12 citations
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TL;DR: Upper and lower bounds for the number of independent sets in a unicyclic graph in terms of its order are determined and the extremal graphs are characterized.
81 citations
TL;DR: The maximum number of cliques in a graph for the following graph classes is determined: graphs with n vertices and m edges, d-degenerate graphs, and planar graphs.
Abstract: A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m edges; (2) graphs with n vertices, m edges, and maximum degree Δ; (3) d-degenerate graphs with n vertices and m edges; (4) planar graphs with n vertices and m edges; and (5) graphs with n vertices and no K5-minor or no K3,3-minor. For example, the maximum number of cliques in a planar graph with n vertices is 8(n − 2).
81 citations
TL;DR: In this article, the problem of determining the largest number of maximum independent sets of a graph of order n is studied, and solutions to this problem are given for various classes of graphs, including general graphs, trees, forests, (connected) graphs with at most one cycle, connected graphs and triangle-free graphs.
Abstract: In this paper, we study the problem of determining the largest number of maximum independent sets of a graph of order n. Solutions to this problem are given for various classes of graphs, including general graphs, trees, forests, (connected) graphs with at most one cycle, connected graphs and triangle-free graphs. Extremal graphs achieving the maximum values are also given.
51 citations
TL;DR: The Maximum Independent Set, which has not been used previously in any summarization study, has been utilized within the context of this study and a text processing tool is suggested in order to preserve the semantic cohesion between sentences in the representation stage of introductory texts.
48 citations
TL;DR: In this article, the authors considered the problem of determining the number of vertex independent sets, and showed that the problem is NP-hard and presented several upper and lower bounds in terms of order, size or independence number.
Abstract: We consider the number of vertex independent sets $i(G)$. In general, the problem of determining the value of $i(G)$ is $NP$-complete. We present several upper and lower bounds for $i(G)$ in terms of order, size or independence number. We obtain improved bounds for $i(G)$ on restricted graph classes such as the bipartite graphs, unicyclic graphs, regular graphs and claw-free graphs.
31 citations