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Enumeration of Labeled Bi-Block Graphs
AbstractA bi-block graph is a connected graph in which all blocks are complete bipartite graphs. Labeled bi-block graphs and bridgeless bi-block...
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Mean Distance on Metric Graphs
We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties...
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Functionality of Box Intersection Graphs
Functionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In...
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Total Cut Complexes of Graphs
Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the total k-cut complex of a graph G to be the simplicial complex whose...
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Minimal graphs in Riemannian spaces
In this treatise, we discuss existence and uniqueness questions for parametric minimal surfaces in Riemannian spaces, which represent minimal graphs....
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On atomic cliques in temporal graphs
Atomic cliques were introduced recently to analyze disease progression in temporal comorbidity graphs. Informally, an atomic clique is a clique that...
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A stability result for translating spacelike graphs in Lorentz manifolds
In this paper, we investigate spacelike graphs defined over a domain Ω ⊂ M n in the Lorentz manifold M n × ℝ with the metric −d s 2 + σ , where M n is a...
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Weakly Saturated Subgraphs of Random Graphs
AbstractIn this paper, we study weak saturation numbers of binomial random graphs. We proved stability of the weak saturation for several pattern...
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Coloring Graphs on Surfaces
The coloring of maps or, equivalently, the coloring of graphs on surfaces is one of the most popular topics in graph coloring theory. This chapter...
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Cubic directed graphs with application
The purpose of this article is to present the Laplacian energy of cubic graphs and cubic directed graphs by analyzing the eigenvalues of the...
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A measure-theoretic representation of graphs
Inspired by the notion of action convergence in graph limit theory, we introduce a measure-theoretic representation of matrices, and we use it to...
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Investigation of Statistics of Nearest Neighbor Graphs
AbstractThis paper describes some statistical properties of the nearest neighbor graphs (NNGs). We study the sample distributions of graphs by the...
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On triangle-free graphs with rank 7
If G does not contain triangle as induced subgraph, then G is called triangle-free. In this paper, by using the congruent vertices of I-. II- and...
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The prime graphs of groups with arithmetically small composition factors
We continue the study of prime graphs of finite groups, also known as Gruenberg–Kegel graphs. The vertices of the prime graph of a finite group are...
