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Anticenter of Profiles in Products of Graphs
A profile on a graph G is a sequence of vertices in which repetitions are allowed. The anticenter of a profile in G is the set of vertices in G that...
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The Complete Classification of Graphs whose Second Largest Eigenvalue of the Eccentricity Matrix is Less Than 1
The eccentricity matrix of a graph is obtained from the distance matrix by kee** the entries that are largest in their row or column, and replacing...
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Steiner Wiener index of Line graphs
Let S be a set of vertices of a connected graph G . The Steiner distance of S is the minimum size among all connected subgraphs whose vertex sets...
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On Graphs and Structural Formulas of the Mechanisms Theory
AbstractStructural formulas in the theory of mechanisms are formulas expressing the number of degrees of freedom of a device in terms of the numbers...
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Computing a maximum clique in geometric superclasses of disk graphs
In the 90’s Clark, Colbourn and Johnson wrote a seminal paper where they proved that maximum clique can be solved in polynomial time in unit disk...
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Combinatorial Properties and Recognition of Unit Square Visibility Graphs
Unit square visibility graphs (USV) are described by axis-parallel visibility between unit squares placed in the plane. If the squares are required...
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Expressivity of Geometric Inhomogeneous Random Graphs—Metric and Non-metric
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bläsius et al. have proposed a...
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Excluded Volume Graphs
Assume that we have a set of points distributed in the 2d plane. These points will be the nodes of the graph and the main idea for excluded volume...
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Factors with Red–Blue Coloring of Claw-Free Graphs and Cubic Graphs
Among some results, we prove the following two theorems. (i) Let G be a connected claw-free graph. We arbitrarily color every vertex of G red or blue...
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The Maximum Clique Problem for Permutation Hamming Graphs
This paper explores a new approach to reduce the maximum clique problem associated with permutation Hamming graphs to smaller clique problems. The...
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Effective divisor classes on metric graphs
We introduce the notion of semibreak divisors on metric graphs and prove that every effective divisor class (of degree at most the genus) has a...
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On Total and Regular Graphs of a Polynomial
A regular graph of the ring of n × n matrices over a field is a graph whose vertices are nonsingular matrices. Two different matrices are adjacent if...
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Parameterized codes over graphs
In this article we review known results on parameterized linear codes over graphs, introduced by Rentería et al. (Finite Fields Appl 17(1):81–104,...
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Accessibility percolation on Cartesian power graphs
A fitness landscape is a map** from a space of discrete genotypes to the real numbers. A path in a fitness landscape is a sequence of genotypes...
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Relations between scaling exponents in unimodular random graphs
We investigate the validity of the “Einstein relations” in the general setting of unimodular random networks. These are equalities relating scaling...
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Anti-van der Waerden Numbers on Graphs
In this paper arithmetic progressions on the integers and the integers modulo n are extended to graphs. A k -term arithmetic progression of a graph G (
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Ricci-flat Graphs with Girth Four
Lin-Lu-Yau introduced a notion of Ricci curvature for graphs and obtained a complete classification for all Ricci-flat graphs with girth at least...