On the connectivity of Cartesian product of graphs
نویسندگان
چکیده
منابع مشابه
Connectivity of Cartesian product graphs
Use vi , i , i , i to denote order, connectivity, edge-connectivity and minimum degree of a graphGi for i=1, 2, respectively. For the connectivity and the edge-connectivity of the Cartesian product graph, up to now, the best results are (G1×G2) 1+ 2 and (G1×G2) 1+ 2. This paper improves these results by proving that (G1×G2) min{ 1+ 2, 2+ 1} and (G1×G2)= min{ 1+ 2, 1v2, 2v1} ifG1 andG2 are conne...
متن کاملRestricted Connectivity of Cartesian Product Graphs
For a connected graph G = (V (G), E(G)), a vertex set S ⊆ V (G) is a k-restricted vertex-cut if G − S is disconnected such that every component of G − S has at least k vertices. The k-restricted connectivity κk(G) of the graph G is the cardinality of a minimum k-restricted vertex-cut of G. In this paper, we give the 3-restricted connectivity and the 4-restricted connectivity of the Cartesian pr...
متن کاملThe reliability Wiener number of cartesian product graphs
Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...
متن کاملSecret Sharing Based On Cartesian product Of Graphs
The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of graphs. We seek to prove that the information ratio of prism graphs $Y_{n}$ are equal to $frac{7}{4}$ for any $ngeq 5$, and we will gave a partial answer to a question of Csirmaz cite{CL}. We will also study the information ratio of two other families $C_{m}times C_{n}$ a...
متن کاملConnectivity and super-connectivity of Cartesian product graphs
This paper determines that the connectivity of the Cartesian product G1 G2 of two graphs G1 and G2 is equal to min{κ1v2, κ2v1, δ1 + δ2}, where vi, κi, δi is the order, the connectivity and the minimum degree of Gi, respectively, for i = 1, 2, and gives some necessary and sufficient conditions for G1 G2 to be maximally connected and super-connected.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2013
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.313.e10