相关论文: Cordial Deficiency
We consider nonregular graphs having precisely three distinct eigenvalues. The focus is mainly on the case of graphs having two distinct valencies and our results include constructions of new examples, structure theorems, valency…
We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of…
We prove new lower and upper bounds on the higher gonalities of finite graphs. These bounds are generalizations of known upper and lower bounds for first gonality to higher gonalities, including upper bounds on gonality involving…
Systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity. The two measures--one well-known and…
Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions…
We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomial.
We compute the elementary divisors of the adjacency and Laplacian matrices of families of polar graphs. These graphs have as vertices the isotropic one-dimensional subspaces of finite vector spaces with respect to non-degenerate forms, with…
We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…
Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious labelings \cite{Hovey}. If $A$ is an Abelian group, then a labeling $f \colon V (G) \rightarrow A$ of the vertices of some graph $G$ induces an edge…
A graph is chordal if it does not contain an induced cycle of length greater than three. We determine the minimum size of a chordal graph with given order and minimum degree. In doing so, we have discovered interesting properties of chordal…
We introduce M\"obius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and M\"obius strip features. We identify the resulting diagram…
A weak order on the set of maximal chains of the non-crossing partition lattice is introduced and studied. A $0$-Hecke algebra action is used to compute the radius of the graph on these chains in which two chains are adjacent if they differ…
In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically…
Chordal graphs are important in algorithmic graph theory. Chordal digraphs are a digraph analogue of chordal graphs and have been a subject of active studies recently. Unlike chordal graphs, chordal digraphs lack many structural properties…
A platypus graph is a non-hamiltonian graph for which every vertex-deleted subgraph is traceable. They are closely related to families of graphs satisfying interesting conditions regarding longest paths and longest cycles, for instance…
We investigate character degree graphs of solvable groups. In particular, we provide general results that can be used to eliminate which degree graphs can occur as solvable groups. Finally, we show a specific family of graphs cannot occur…
We characterize positive critical Hardy weights for general Laplacians on weighted graphs. We then apply this result to fractional Laplacians on general graphs and use the characterization to identify an optimal Hardy weight under suitable…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…
Hefner [K. A. S. Hefner, K. F. Jones, S. -R. Kim, R. J. Lundgren and F. S. Roberts: $(i,j)$ competition graphs, Discrete Applied Mathematics, 32, (1991) 241-262] characterized acyclic digraphs each vertex of which has inderee and outdegree…