3 citations · 7 across the 14 of their papers we have counts for
13 papers · 1 filter
The integer -domination number of grids
Jia-Ying Lee, Chia-An Liu
For positive integers and , the grid graph is the Cartesian product of the path graph on vertices and the path graph on vertices. An integer $\…
Counterexamples of the Bhattacharya-Friedland-Peled conjecture
Yen-Jen Cheng, Chia-An Liu, Chih-wen Weng
The Brauldi-Hoffman conjecture, proved by Rowlinson in 1988, characterized the graph with maximal spectral radius among all simple graphs with prescribed number of edges. In 2008,…
Ramsey Properties for -shaped Posets in the Boolean Lattices
Hong-Bin Chen, Wei-Han Chen, Yen-Jen Cheng +2
Given posets , let the {\em Boolean Ramsey number} be the minimum number such…
Domination in the Sierpiński graphs S(K_n,t)
Chia-An Liu
Different types of domination on the Sierpiński graphs S(K_n,t) will be studied in this paper. More precisely, we propose a minimal dominating set for S(K_n,t) so that the exact va…
The Boolean Rainbow Ramsey Number of Antichains, Boolean Posets, and Chains
Hong-Bin Chen, Yen-Jen Cheng, Wei-Tian Li +1
Motivated by the paper of Axenovich and Walzer [2], we study the Ramsey-type problems on the Boolean lattices. Given posets and , we look for the smallest Boolean lattice $\…
On the integer {k}-domination number of circulant graphs
Yen-Jen Cheng, Hung-Lin Fu, Chia-an Liu
Let be a simple undirected graph. is a circulant graph defined on with difference set provided…
On the degree pairs of a graph
Yu-pei Huang, Chia-an Liu, Chih-wen Weng
Let G be a simple graph without isolated vertices. For a vertex i in G, the degree d_i is the number of vertices adjacent to i and the average 2-degree m_i is the mean of the degre…
A family of group divisible designs with arbitrary block sizes
Yu-pei Huang, Chia-an Liu, Yaotsu Chang +1
Recently, a construction of group divisible designs (GDDs) derived from the decoding of quadratic residue (QR) codes was given. In this paper, we extend the idea to obtain a new fa…
A construction of group divisible designs with zero block sum
Chong-Dao Lee, Yaotsu Chang, Chia-an Liu
This paper gives a construction of group divisible designs on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which is motivated from the decoding of…
Spectral characterizations of two families of nearly complete bipartite graphs
Chia-an Liu, Chih-wen Weng
It is not hard to find many complete bipartite graphs which are not determined by their spectra. We show that the graph obtained by deleting an edge from a complete bipartite graph…
A (forgotten) upper bound for the spectral radius of a graph
Clive Elphick, Chia-an Liu
The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating f…
Spectral Radius of Bipartite Graphs
Chia-an Liu, Chih-wen Weng
Let k, p, q be positive integers with k < p < q+1. We prove that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph Kp,q of bipartit…
Spectral Radius and Degree Sequence of a Graph
Chia-an Liu, Chih-wen Weng
Let G be a simple connected graph of order n with degree sequence d_1, d_2, ..., d_n in non-increasing order. The spectral radius rho(G) of G is the largest eigenvalue of its adjac…