Results 11 to 20 of about 789,258 (121)
Potential Role of Menstrual Fluid‐Derived Small Extracellular Vesicle Proteins in Endometriosis Pathogenesiss [PDF]
Journal of Extracellular Vesicles, Volume 14, Issue 3, March 2025.ABSTRACT Endometriosis, a chronic debilitating disease affects 1 in 7–10 girls and women, who have symptoms of severe chronic pain and subfertility and significantly impacts the overall quality of life. Currently, no effective early diagnostic methods are available for early stages of endometriosis.
Shanti Gurung +7 more
wiley +2 more sources
Ars Mathematica Contemporanea, 17(2):349--368, 2019, 2018 We introduce a notion of a girth-regular graph as a $k$-regular graph for which there exists a non-descending sequence $(a_1, a_2, \dots, a_k)$ (called the signature) giving, for every vertex $u$ of the graph, the number of girth cycles the edges with end-vertex $u$ lie on.
arxiv +1 more source
2-distance 4-coloring of planar subcubic graphs with girth at least 21 [PDF]
Discrete Mathematics & Theoretical Computer Science, vol. 26:3,
Graph Theory (March 5, 2025) dmtcs:7563, 2021 A $2$-distance $k$-coloring of a graph is a proper vertex $k$-coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a $2$-distance $4$-coloring for planar subcubic graphs with girth at least 21. We also show a construction of a planar subcubic graph of girth 11 that is not $2$-distance $4$-colorable.
arxiv +1 more source
On the Minimum Order of Extremal Graphs to have a Prescribed Girth [PDF]
, 2007 We show that any n‐vertex extremal graph G without cycles of length at most k has girth exactly $k+1$ if $k\ge 6$ and $n>(2(k-2)^{k-2}+k-5)/(k-3)$. This result provides an improvement of the asymptotical known result by Lazebnik and Wang [J. Graph Theory,
Balbuena, C., García Vázquez, Pedro
core +1 more source
The missing Moore graph as an optimization problem
EURO Journal on Computational Optimization, 2023 It has been an open question for 6 decades whether a Moore graph of diameter 2 and degree 57 exists. In this paper the question is posed as an optimization problem and an algorithm is described.
Derek H. Smith, Roberto Montemanni
doaj
Total Domination Versus Paired-Domination in Regular Graphs
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph
Cyman Joanna +4 more
doaj +1 more source
Attainable bounds for algebraic connectivity and maximally-connected regular graphs [PDF]
arXiv, 2023 We derive attainable upper bounds on the algebraic connectivity (spectral gap) of a regular graph in terms of its diameter and girth. This bound agrees with the well-known Alon-Boppana-Friedman bound for graphs of even diameter, but is an improvement for graphs of odd diameter.
arxiv
Computing Graph Roots Without Short Cycles [PDF]
, 2009 Graph G is the square of graph H if two vertices x, y have an edge in G if and only if x, y are of distance at most two in H. Given H it is easy to compute its square H2, however Motwani and Sudan proved that it is NP-complete to determine if a given ...
Farzad, Babak +3 more
core +3 more sources
, 2018 Cages, defined as regular graphs with minimum number of nodes for a given girth, are well-studied in graph theory. Trapping sets are graphical structures responsible for error floor of low-density parity-check (LDPC) codes, and are well investigated in ...
Banihashemi, Amir H., Dehghan, Ali
core +1 more source
On the girth of random Cayley graphs [PDF]
Random Structures Algorithms 35 (2009), no. 1, 100-117, 2007 We prove that random d-regular Cayley graphs of the symmetric group asymptotically almost surely have girth at least (log_{d-1}|G|)^{1/2}/2 and that random d-regular Cayley graphs of simple algebraic groups over F_q asymptotically almost surely have girth at least log_{d-1}|G|/dim(G). For the symmetric p-groups the girth is between log log |G| and (log|
arxiv +1 more source