
A radio labeling of a simple connected graph
The radio number of a graph
It is known that an ordered
Compressed sensing (CS), which is a rising technique of signal processing, successfully manages the huge expenditure of increasing the sampling rate as well as the intricate issues to our work. Hence, more and more attention has been paid to CS during recent years. In this paper, we construct a family of error-correcting pooling designs based on singular linear space over finite fields, which can be efficiently applied to signal processing in terms of CS.
It is proven that for all positive integers
In 1770, Waring conjectured that for each positive integer
As a natural question arising from this problem, Johnson and Laughlin [1] proposed what they called an anti-Waring conjecture, which is the following: If
Johnson and Laughlin further posed the question of whether given any positive integers
We consider an optimization problem motivated by the tradeoff between connectivity and resilience in key predistribution schemes (KPS) for sensor networks that are based on certain types of combinatorial designs. For a specific class of designs, we show that there is no real disadvantage in requiring the underlying design to be regular.
We define three new pebbling parameters of a connected graph
A set
A graph
A path
In this paper we concentrate on the study of how
Finally we study
In all these cases we give bounds on the parameter
Given a graph
A DI-pathological graph is a graph in which every minimum dominating set intersects every maximal independent set. DI-pathological graphs are related to the Inverse Domination Conjecture; hence, it is useful to characterize properties of them. One characterization question is how large or small a graph can be relative to the domination number. Two useful characterizations of size seem relevant, namely the number of vertices and the number of edges. In this paper, we provide two results related to this question. In terms of the number of vertices, we show that every connected, DI-pathological graph has at least
A dominating set in a graph
We consider edge-colorings of complete graphs in which each color induces a subgraph that does not contain an induced copy of
Multi-sender authentication codes allow a group of senders to construct an authenticated message for a receiver such that the receiver can verify the authenticity of the received message. In this paper, we construct one multi-sender authentication code from polynomials over finite fields. Some parameters and the probabilities of deceptions of this code are also compute
For graphs
If
Let
Let
In this paper, we construct
The spread of a graph
A
Informally, a set is an
Eternal vertex covers are shown to be closed under taking supersets and a lower bound for
An optimal attack/defense strategy is determined for a set of size
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