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202views Education» more  DM 2011»
9 years 4 months ago
Two-ended regular median graphs
We show that regular median graphs of linear growth are the Cartesian product of finite hypercubes with the two-way infinite path. Such graphs are Cayley graphs and have only tw...
Wilfried Imrich, Sandi Klavzar
100views more  TKDE 1998»
10 years 1 months ago
Scalability Analysis of Declustering Methods for Multidimensional Range Queries
E cient storage and retrieval of multi-attribute datasets have become one of the essential requirements for many data-intensive applications. The Cartesian product le has been kno...
Bongki Moon, Joel H. Saltz
85views more  COMBINATORICS 2000»
10 years 1 months ago
Inequality Related to Vizing's Conjecture
Let (G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that (G)(H) 2(G H) for all simple graphs G and H. 2000 Math...
W. Edwin Clark, Stephen Suen
91views more  ENDM 2007»
10 years 1 months ago
Game chromatic number of Cartesian product graphs
We find exact values for the game chromatic number of the Cartesian product graphs Sm Pn, Sm Cn, P2 Wn, and P2 Km,n. This extends previous results of Bartnicki et al. on the game...
Iztok Peterin
76views more  JIIS 2006»
10 years 1 months ago
Holes in joins
A join of two relations in real databases is usually much smaller than their cartesian product. This means that most of the combinations of tuples in the crossproduct of the respe...
Jarek Gryz, Dongming Liang
97views more  DM 2007»
10 years 1 months ago
Recognizing Cartesian products in linear time
We present an algorithm that determines the prime factors of connected graphs with respect to the Cartesian product in linear time and space. This improves a result of Aurenhammee...
Wilfried Imrich, Iztok Peterin
62views more  DAM 2007»
10 years 1 months ago
Cancellation properties of products of graphs
This note extends results of Fern´andez, Leighton, and L´opez-Presa on the uniqueness of rth roots for disconnected graphs with respect to the Cartesian product to other product...
Wilfried Imrich, Sandi Klavzar, Douglas F. Rall
103views more  JGT 2008»
10 years 1 months ago
Game coloring the Cartesian product of graphs
: This article proves the following result: Let G and G be graphs of orders n and n , respectively. Let G be obtained from G by adding to each vertex a set of n degree 1 neighbors....
Xuding Zhu
50views more  COMBINATORICS 2007»
10 years 1 months ago
Perfect Dominating Sets in the Cartesian Products of Prime Cycles
We study the structure of a minimum dominating set of Cn 2n+1, the Cartesian product of n copies of the cycle of size 2n + 1, where 2n + 1 is a prime.
Hamed Hatami, Pooya Hatami
10 years 1 months ago
The distinguishing number of Cartesian products of complete graphs
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d labels that is preserved only by a trivial automorphism. We prove that Cartesi...
Wilfried Imrich, Janja Jerebic, Sandi Klavzar