Results 51 to 60 of about 789,258 (121)
Ramanujan Graphs with Small Girth [PDF]
arXiv, 2003 We construct an infinite family of (q+1)-regular Ramanujan graphs X_n of girth 1. We also give covering maps X_{n+1} --> X_n such that the minimal common covering of all the graphs is the universal covering tree.
arxiv
On Almost Well-Covered Graphs of Girth at Least 6
, 2018 We consider a relaxation of the concept of well-covered graphs, which are graphs with all maximal independent sets of the same size. The extent to which a graph fails to be well-covered can be measured by its independence gap, defined as the difference ...
Ekim, Tınaz +3 more
core +1 more source
Dense circuit graphs and the planar Turán number of a cycle
Journal of Graph Theory, Volume 108, Issue 1, Page 27-38, January 2025.Abstract The planar Turán number ex P ( n , H ) of a graph H is the maximum number of edges in an n‐vertex planar graph without H as a subgraph. Let C k denote the cycle of length k. The planar Turán number ex P ( n , C k ) is known for k ≤ 7. We show that dense planar graphs with a certain connectivity property (known as circuit graphs) contain large ...
Ruilin Shi, Zach Walsh, Xingxing Yu
wiley +1 more source
A note on circular chromatic number of graphs with large girth and similar problems [PDF]
, 2014 In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that graphs of large girth excluding a minor are nearly bipartite.
De Mendez, Patrice Ossona +1 more
core +1 more source
CAT(0) and cubulated Shephard groups
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well‐known result that Coxeter groups are CAT(0)$\mathrm{CAT}(0)$ to a class of Shephard ...
Katherine M. Goldman
wiley +1 more source
The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups $S_{2^n}$ on diagonal bases [PDF]
arXiv, 2018 A diagonal base of a Sylow 2-subgroup $P_n(2)$ of symmetric group $S_{2^n}$ is a minimal generating set of this subgroup consisting of elements with only one non-zero coordinate in the polynomial representation. For different diagonal bases Cayley graphs of $P_n(2)$ may have different girths (i.e.
arxiv
Constructions and Enumeration Methods for Cubic Graphs and Trees [PDF]
, 2013 The goal of this thesis is to study two related problems that, in the broadest terms, lie in a branch of mathematics called graph theory. The first problem examines some new techniques for constructing a Hamilton graph of least possible order and having ...
Gilliland, Erica R.
core +1 more source
Extremal Values on the General Degree–Eccentricity Index of Unicyclic Graphs of Fixed Diameter
Journal of Mathematics, Volume 2025, Issue 1, 2025.For a connected graph G and two real numbers a, b, the general degree–eccentricity index of G is given by DEIa,bG=∑v∈VGdGavecGbv, where V(G) represent the vertex set of graph G, dG(v) denotes the degree of vertex v, and ecG(v) is the eccentricity of v in G, that is, the maximum distance from v to another vertex of G. This index generalizes several well‐
Mesfin Masre, G. Muhiuddin
wiley +1 more source
The trivial lower bound for the girth of $S_n$ [PDF]
arXiv, 2017 Consider the Cayley graph of $S_n$ generated by a random pair of elements $x,y$. Conjecturally, the girth of this graph is $\Omega(n \log n)$ with probability tending to $1$ as $n\to\infty$. We show that it is at least $\Omega(n^{1/3})$.
arxiv
Positive sweet corn response with selected climate‐smart agricultural practices
Agrosystems, Geosciences &Environment, Volume 7, Issue 4, December 2024.Abstract To sustain agriculture for future generations and reduce the adverse impacts on soil health and the environment, there is a need to adopt sustainable and climate‐smart agricultural practices. A field experiment was conducted to study the effects of organic amendments (chicken and dairy manures and biochar) on the soil physicochemical ...
Binita Thapa +7 more
wiley +1 more source