Related papers: On strongly regular graph with parameters (65; 32;…
Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…
Strongly chordal graphs are a subclass of chordal graphs. The interest in this subclass stems from the fact that many problems which are NP-complete for chordal graphs are solvable in polynomial time for this subclass. However, we are not…
A graph is called 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we establish a local property of 1-planar graphs which describes the structure in the neighborhood of small…
We give the first specific conjectures on how frequently graphs satisfy sufficient conditions for being uniquely characterized by spectral information. These conjectures arise from a theoretical framework that we developed based on…
In this paper we unify several existing regularity conditions for graphs, including strong regularity, $k$-isoregularity, and the $t$-vertex condition. We develop an algebraic composition/decomposition theory of regularity conditions. Using…
We report about the results of the application of modern computer algebra tools for construction of directed strongly regular graphs. The suggested techniques are based on the investigation of non-commutative association schemes and Cayley…
Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. Associative arrays unify and simplify these different approaches into a common…
In this paper, we propose a path following replicator dynamic, and investigate its potentials in uncovering the underlying cluster structure of a graph. The proposed dynamic is a generalization of the discrete replicator dynamic. The…
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their…
In this paper convolutional codes with cyclic structure will be investigated. These codes can be understood as left principal ideals in a suitable skew-polynomial ring. It has been shown in [3] that only certain combinations of the…
Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…
We apply Godsil-McKay switching to the symplectic graphs over $\mathbb{F}_2$ with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new…
We describe a general construction of strongly regular graphs from the collinearity graph of a finite classical polar spaces of rank at least $3$ over a finite field of order $q$. We show that these graphs are non-isomorphic to the…
We introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection to designs over finite fields, and present a classification.
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
A matching set $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. In this paper we consider some parameters related to the matching of regular graphs. We find the sixth coefficient of the…
Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in…
A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is…
In this paper we analyze the practical implications of Szemer\'edi's regularity lemma in the preservation of metric information contained in large graphs. To this end, we present a heuristic algorithm to find regular partitions. Our…