Applying the Kirchhoff Relations in Proofs of Theorems on Graph Operations that Do Not Affect the Structure of the Sandpile Groups of Graphs
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-017-3414-4
Abstract: New proofs of theorems on graph operations that do not affect the structure of the sandpile groups of graphs are suggested. The proofs are based on the isomorphism between the sandpile group and the Kirchhoff… read more here.
Keywords: theorems graph; affect structure; operations affect; structure sandpile ... See more keywords
Index theorems for graph-parametrized optimal control problems
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DOI: 10.1088/1361-6544/acc5d4
Abstract: In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse… read more here.
Keywords: parametrized optimal; index; graph parametrized; theorems graph ... See more keywords
Some deterministic and random fixed point theorems on a graph
Sign Up to like & getrecommendations! Published in 2018 at "Random Operators and Stochastic Equations"
DOI: 10.1515/rose-2018-0019
Abstract: Abstract We present the random version of the classical Banach contraction principle and some of its generalizations to ordered metric spaces or in metric spaces endowed with a graph. read more here.
Keywords: theorems graph; random; random fixed; deterministic random ... See more keywords