scholarly journals A Stronger Lower Bound on Parametric Minimum Spanning Trees

2021 ◽  
pp. 343-356
Author(s):  
David Eppstein
Keyword(s):  
Lower Bound ◽  
Spanning Trees ◽  
Minimum Spanning Trees

scholarly journals A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning Trees

2020 ◽  
Vol 16 (1) ◽  
pp. 1-27
Author(s):  
Gopal Pandurangan ◽  
Peter Robinson ◽  
Michele Scquizzato
Keyword(s):  
Distributed Algorithm ◽  
Spanning Trees ◽  
Minimum Spanning Trees

ON THE NORMALISED LAPLACIAN SPECTRUM, DEGREE-KIRCHHOFF INDEX AND SPANNING TREES OF GRAPHS

2015 ◽  
Vol 91 (3) ◽  
pp. 353-367 ◽  
Author(s):  
JING HUANG ◽  
SHUCHAO LI
Keyword(s):  
Lower Bound ◽  
Characteristic Polynomial ◽  
Regular Graph ◽  
Spanning Trees ◽  
Line Graph ◽  
Laplacian Spectrum ◽  
Kirchhoff Index ◽  
Subdivision Graph ◽  
Number Of Spanning Trees ◽  
Sharp Lower Bound

Given a connected regular graph $G$, let $l(G)$ be its line graph, $s(G)$ its subdivision graph, $r(G)$ the graph obtained from $G$ by adding a new vertex corresponding to each edge of $G$ and joining each new vertex to the end vertices of the corresponding edge and $q(G)$ the graph obtained from $G$ by inserting a new vertex into every edge of $G$ and new edges joining the pairs of new vertices which lie on adjacent edges of $G$. A formula for the normalised Laplacian characteristic polynomial of $l(G)$ (respectively $s(G),r(G)$ and $q(G)$) in terms of the normalised Laplacian characteristic polynomial of $G$ and the number of vertices and edges of $G$ is developed and used to give a sharp lower bound for the degree-Kirchhoff index and a formula for the number of spanning trees of $l(G)$ (respectively $s(G),r(G)$ and $q(G)$).

Bounded-Angle Minimum Spanning Trees

Algorithmica ◽  
2021 ◽  
Author(s):  
Ahmad Biniaz ◽  
Prosenjit Bose ◽  
Anna Lubiw ◽  
Anil Maheshwari
Keyword(s):  
Spanning Trees ◽  
Minimum Spanning Trees
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