相关论文: The $\rho$-Capacity of a Graph
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph…
In graph theory, knowing the number of complete subgraphs with r vertices that a graph g has, limits the number of its complete subgraphs with s vertices, for s > r. A useful upper bound is provided by the Kruskal-Katona theorem, but this…
We consider the problem of determining the maximum induced density of a graph H in any graph on n vertices. The limit of this density as n tends to infinity is called the inducibility of H. The exact value of this quantity is known only for…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
The upper and lower Nordhaus-Gaddum bounds over all graphs for the power domination number follow from known bounds on the domination number and examples. In this note we improve the upper sum bound for the power domination number…
This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…
The capacity of unifilar finite-state channels in the presence of feedback is investigated. We derive a new evaluation method to extract graph-based encoders with their achievable rates, and to compute upper bounds to examine their…
Shannon-Hartley theorem can accurately calculate the channel capacity when the signal observation time is infinite. However, the calculation of finite-time capacity, which remains unknown, is essential for guiding the design of practical…
We consider three capacity definitions for general channels with channel side information at the receiver, where the channel is modeled as a sequence of finite dimensional conditional distributions not necessarily stationary, ergodic, or…
We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in…
In this paper, we find upper bounds on the open packing and $k$-limited packing numbers with emphasis on the cases $k=1$ and $k=2$. We solve the problem of characterizing all connected graphs on $n$ vertices with $\rho_{o}(G)=n/\delta(G)$…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
In this note, we present a fractional version of Haemers' bound on the Shannon capacity of a graph, which is originally due to Blasiak. This bound is a common strengthening of both Haemers' bound and the fractional chromatic number of a…
Throttling in graphs optimizes a sum or product of resources used, such as the number of vertices in an initial set, and time required, such as the propagation time, to complete a given task. We introduce a new technique to establish sharp…
Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
We define non-commutative versions of the vertex packing polytope, the theta convex body and the fractional vertex packing polytope of a graph, and establish a quantum version of the Sandwich Theorem of Gr\"{o}tschel, Lov\'{a}sz and…
The zero-error capacity of a classical channel is a parameter of its confusability graph, and is equal to the minimum of the values of graph parameters that are additive under the disjoint union, multiplicative under the strong product,…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…