On the weak reconstruction of Cartesian-product graphs

On the weak reconstruction of Cartesian-product graphs

In this paper we reconstruct nontrivial connected Cartesian product graphs from single vertex deleted subgraphs. We show that all one-vertex extensions of a given connected graph H, nite or innnite, to a nontrivial Cartesian product are isomorphic.

The 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...

Secret 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...

On the Weak Reconstruction of Strong Product Graphs

Weak reconstruction of strong product graphs

We prove that the class of nontrivial connected strong product graphs is weakly reconstructible. We also show that any nontrivial connected thin strong product graph can be uniquely reconstructed from each of its one-vertex-deleted deleted subgraphs. © 2006 Elsevier B.V. All rights reserved. MSC: 05C