scholarly journals On the number of disjoint perfect matchings of regular graphs with given edge connectivity

2017 ◽  
Vol 340 (3) ◽  
pp. 305-310
Author(s):  
Hongliang Lu ◽  
Yuqing Lin
Keyword(s):  
Perfect Matchings ◽  
Regular Graphs ◽  
Edge Connectivity

scholarly journals Matching and edge-connectivity in regular graphs

2011 ◽  
Vol 32 (2) ◽  
pp. 324-329 ◽  
Author(s):  
Suil O ◽  
Douglas B. West
Keyword(s):  
Regular Graphs ◽  
Edge Connectivity

Super restricted edge connectivity of regular graphs with two orbits

2012 ◽  
Vol 218 (12) ◽  
pp. 6656-6660 ◽  
Author(s):  
Huiqiu Lin ◽  
Jixiang Meng ◽  
Weihua Yang
Keyword(s):  
Regular Graphs ◽  
Edge Connectivity

scholarly journals The Tau Constant and the Edge Connectivity of a Metrized Graph

10.37236/2934 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Zubeyir Cinkir
Keyword(s):  
Lower Bound ◽  
Algebraic Curves ◽  
Regular Graphs ◽  
Graph Invariants ◽  
Edge Connectivity ◽  
Kirchhoff Index ◽  
Arithmetic Properties

The tau constant is an important invariant of a metrized graph. It has connections to other graph invariants such as Kirchhoff index, and it has applications to arithmetic properties of algebraic curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We prove identities which we call "contraction", "deletion", and "contraction-deletion" identities on a metrized graph. By establishing a lower bound for the tau constant in terms of the edge connectivity, we prove that Baker and Rumely's lower bound conjecture on the tau constant holds for metrized graphs with edge connectivity 5 or more. We show that proving this conjecture for 3-regular graphs is enough to prove it for all graphs.

scholarly journals Spectral Bounds for the Connectivity of Regular Graphs with Given Order

2018 ◽  
Vol 34 ◽  
pp. 428-443 ◽  
Author(s):  
Aida Abiad ◽  
Boris Brimkov ◽  
Xavier Martinez-Rivera ◽  
Suil O ◽  
Jingmei Zhang
Keyword(s):  
Upper Bounds ◽  
Regular Graphs ◽  
Laplacian Eigenvalue ◽  
Edge Connectivity ◽  
Characteristic Path Length ◽  
Largest Eigenvalues ◽  
Spectral Bounds ◽  
Isoperimetric Number ◽  
The Given ◽  
Second Largest Eigenvalue

The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, two upper bounds are presented for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results answer a question of Mohar.

scholarly journals Edge-connectivity of regular graphs with two orbits

2008 ◽  
Vol 308 (16) ◽  
pp. 3711-3716 ◽  
Author(s):  
Fengxia Liu ◽  
Jixiang Meng
Keyword(s):  
Regular Graphs ◽  
Edge Connectivity
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