Dr Joe Ryan

We introduce a new graph-theoretic concept in the area of network monitoring. A set M of vertices of a graph G is a distance-edge-monitoring set if for every edge e of G, there are a vertex x of M and a vertex y of G such that e belongs to all shortest paths between x and y. We denote by dem(G) the smallest size of such a set in G. The vertices of M represent distance probes in a network modeled by G; when the edge e fails, the distance from x to y increases, and thus we are able to detect the failure. It turns out that not only we can detect it, but we can even correctly locate the failing edge. In this paper, we initiate the study of this new concept. We show that for a nontrivial connected graph G of order n, 1=dem(G)=n-1 with dem(G)=1 if and only if G is a tree, and dem(G)=n-1 if and only if it is a complete graph. We compute the exact value of dem for grids, hypercubes, and complete bipartite graphs. Then, we relate dem to other standard graph parameters. We show that dem(G) is lower-bounded by the arboricity of the graph, and upper-bounded by its vertex cover number. It is also upper-bounded by twice its feedback edge set number. Moreover, we characterize connected graphs G with dem(G)=2. Then, we show that determining dem(G) for an input graph G is an NP-complete problem, even for apex graphs. There exists a polynomial-time logarithmic-factor approximation algorithm, however it is NP-hard to compute an asymptotically better approximation, even for bipartite graphs of small diameter and for bipartite subcubic graphs. For such instances, the problem is also unlikely to be fixed parameter tractable when parameterized by the solution size.

The Fourth Industrial Revolution (Industry 4.0), with the help of cyber-physical systems (CPS), the Internet of Things (IoT), and Artificial Intelligence (AI), is transforming the way industrial setups are designed. Recent literature has provided insight about large firms gaining benefits from Industry 4.0, but many of these benefits do not translate to SMEs. The agent-oriented smart factory (AOSF) framework provides a solution to help bridge the gap between Industry 4.0 frameworks and SME-oriented setups by providing a general and high-level supply chain (SC) framework and an associated agent-oriented storage and retrieval (AOSR)-based warehouse management strategy. This paper presents the extended heuristics of the AOSR algorithm and details how it improves the performance efficiency in an SME-oriented warehouse. A detailed discussion on the thorough validation via scenario-based experimentation and test cases explain how AOSR yielded 60¿148% improved performance metrics in certain key areas of a warehouse.

We define f: E(G) ¿{1, 2,...,ke} and f:V (G) ¿{0, 2,..., 2kv} for ke,kv N ¿{0}, where k =max{ke, 2kv}. The labeling f is called a vertex irregular reflexive k-labeling if any vertices have distinct weight which wf(u)¿wf(v) for any vertices in a graph G. The weight of a vertex u V (G) is defined as the sum of the labels of vertex and the labels of all edges incident this vertex. The smallest k for which such labeling exists is called reflexive vertex strength of G, denoted by rvs(G). In this paper, we determine the reflexive vertex strength of gear graphs, book graphs, triangular book graph and the disjoint union of gear graphs.

Wirelength is a salient feature to authenticate the quality of an embedding of a guest graph into a host graph and is used specifically in Very Large Scale Integration (VLSI) layout designs. The chord graph is an influential topology in the sphere of peer-to-peer networks. Thus, it is interesting to study the embedding of chord graphs into networks. In this paper, we have computed the exact wirelength of chord graphs into necklace and windmill graphs. Further, we have developed a linear time algorithm to compute the wirelength.

This survey directs its focus, not on the history of security in statistical databases, but on the contribution of Mirka Miller to this field. It begins with her early work in her PhD thesis in which she formalised the varieties of compromise, introduced a new compromise, the relative compromise, and classified supplementary knowledge. It follows on to include her innovative work in employing combinatorial concepts to formulate the bounds of usability of Audit Expert in both the absolute and relative compromise. It finishes in true Mirka style, leaving the reader with open problems and directions in which this area might progress.

Recent research has motivated the investigation of the weights of ideals in semiring constructions based on semigroups. The present paper introduces Rees semigroups of directed graphs. This new construction is a common generalization of Rees matrix semigroups and incidence semigroups of digraphs. For each finite subsemigroup S of the Rees semigroup of a digraph and for every zero-divisor-free idempotent semiring F with identity element, our main theorem describes all ideals J in the semigroup semiring F0[S] such that J has the largest possible weight.

This article continues the investigation of matrix constructions motivated by their applications to the design of classification systems. Our main theorems strengthen and generalize previous results by describing all centroid sets for classification systems that can be generated as one-sided ideals with the largest weight in structural matrix semirings. Centroid sets are well known in data mining, where they are used for the design of centroid-based classification systems, as well as for the design of multiple classification systems combining several individual classifiers.

A simple graph G = (V; E) admits an H-covering if every edge in E belongs to at least one subgraph of G isomorphic to a given graph H. Then the graph G is (a; d)-H-antimagic if there exists a bijection f : ¿ E ¿ {1, 2, V + E} such that, for all subgraphs H0 of G isomorphic to H, the H-weights, wtf (H) =¿vv(H') f(v)+¿e¿(H') f(e) form an arithmetic progression with the initial term a and the common difference d. When f (V) = {1; 2 V}, then G is said to be super (a; d)-H-antimagic. In this paper, we study super (a, d)-H-antimagic labellings of a disjoint union of graphs for d = E(H) -V(H).

For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . ., |V(G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total labeling is called edge-antimagic total (vertexantimagic total) if all edge-weights (vertex-weights) are pairwise distinct. If a labeling is simultaneously edge-antimagic total and vertex-antimagic total it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is called a totally antimagic total graph.

An antimagic labeling of a graph with q edges is a bijection from the set of edges of the graph to the set of positive integers (Formula presented.) such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. The join graph G + H of the graphs G and H is the graph with (Formula presented.) and (Formula presented.). The complete bipartite graph K<inf>m,n</inf> is an example of join graphs and we give an antimagic labeling for (Formula presented.). In this paper we also provide constructions of antimagic labelings of some complete multipartite graphs.

Lladó and Moragas ['Cycle-magic graphs', Discrete Math. 307 (2007), 2925¿2933] showed the cyclic-magic and cyclic-supermagic behaviour of several classes of connected graphs. They discussed cycle-magic labellings of subdivided wheels and friendship graphs, but there are no further results on cycle-magic labellings of other families of subdivided graphs. In this paper, we find cycle-magic labellings for subdivided graphs. We show that if a graph has a cycle-(super)magic labelling, then its uniform subdivided graph also has a cycle-(super)magic labelling. We also discuss some cycle-supermagic labellings for nonuniform subdivided fans and triangular ladders.

A simple graph G admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. An (a, d)-H-antimagic total labeling of a graph G admitting an H-covering is a bijective function from the vertex set V(G) and the edge set E(G) of the graph G onto the set of integers {1, 2, ..., |V(G)|+|E(G)|} such that for all subgraphs H' isomorphic to H, the sum of labels of all the edges and vertices belonging to H' constitute the arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super cycle-antimagic total labelings of wheel.

The aim of this paper is to prove that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest weight, and the distance of J is equal to its weight. This result is surprising and unexpected, because examples show that distances of arbitrary centroid sets in incidence semirings may be strictly less than their weights. The investigation of the distances of centroid sets in incidence semirings of digraphs has been motivated by the information security applications of centroid sets.

Let G(V,E) be a simple connected graph. A set S¿V is a power dominating set (PDS) of G, if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of a PDS of a graph G is the power domination number ¿p(G). In this paper, we establish a fundamental result that would provide a lower bound for the power domination number of a graph. Further, we solve the power domination problem in polyphenylene dendrimers, Rhenium Trioxide (ReO3) lattices and silicate networks.

We describe and implement a computer-based method to find large multi-loop graphs with given degree and diameter. For some values of degree and diameter, our algorithm produces the largest known circulant graphs. We summarize our findings in a table.

For an integer k = 1, we say that a (finite simple undirected) graph G is k-distance-locally disconnected, or simply k-locally disconnected if, for any x ¿ V (G), the set of vertices at distance at least 1 and at most k from x induces in G a disconnected graph. In this paper we study the asymptotic behavior of the number of edges of a k-locally disconnected graph on n vertices. For general graphs, we show that this number is I(n2) for any fixed value of k and, in the special case of regular graphs, we show that this asymptotic rate of growth cannot be achieved. For regular graphs, we give a general upper bound and we show its asymptotic sharpness for some values of k. We also discuss some connections with cages.

Let G = (V, E) be a finite (non-empty) graph. A monograph is a graph in which all vertices are assigned distinct real number labels so that the positive difference of the end-vertices of every edge is also a vertex label. In this paper we study the properties of monographs and construct signatures for several classes of graph, such as cycles, cycles with chord, fan graphs Fn, kite graphs, chains of monographs and necklaces of monographs.

A statistical database system is a system that contains information about individuals, companies or organisations that enables authorized users to retrieve aggregate statistics such as mean and count. The regulation of a statistical database involves limiting the use of the database so that no sequence of queries is sufficient to infer protected information about an individual. The database is said to be compromised when individual confidential information is obtained as a result of a statistical query. Devices to protect against compromise include adding noise to the data or restricting a query. While effective, these techniques are sometimes too strong in that legitimate compromises for reasons of public safety are always blocked. Further, a statistical database can be often be compromised with some knowledge about the database attributes (working knowledge), the real world (supplementary knowledge) or the legal system (legal knowledge). In this paper we illustrate that a knowledge based system that represents working, supplementary and legal knowledge can contribute to the regulation of a statistical database.

The term mode graph was introduced by Boland, Kauffman and Panrong [2] to define a connected graph G such that, for every pair of vertices v, w in G, the number of vertices with eccentricity e(v) is equal to the number of vertices with eccentricity e(w). As a natural extension to this work, the concept of an antimode graph was introduced to describe a graph for which if e(v) ¿ e(w) then the number of vertices with eccentricity e(w) is not equal to the number of vet tices with eccentricity e(w). In this paper we determine the existence of some classes of antimode graphs, namely equisequential and (a, d)-antimode graphs.