Applying the Kirchhoff Relations in Proofs of Theorems on Graph Operations that Do Not Affect the Structure of the Sandpile Groups of Graphs
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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
f-Polynomial on Some Graph Operations
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DOI: 10.3390/math7111074
Abstract: Given any function f : Z + → R + , let us define the f-index I f ( G ) = ∑ u ∈ V ( G ) f ( d u ) and… read more here.
Keywords: graph; graph operations; polynomial graph;