The Jacobsthal and Jacobsthal-Lucas sequences associated with pseudo graphs
Fatih Y{\i}lmaz, Durmu\c{s} Bozkurt
TL;DR
This paper introduces two directed pseudo graphs and demonstrates that the permanents of their adjacency matrices correspond to Jacobsthal and Jacobsthal-Lucas numbers, linking graph theory with these special sequences.
Contribution
It defines new pseudo graphs and establishes a novel connection between their adjacency matrix permanents and Jacobsthal sequences.
Findings
Permanents of adjacency matrices equal Jacobsthal numbers
Permanents of adjacency matrices equal Jacobsthal-Lucas numbers
Links between pseudo graph structures and special number sequences
Abstract
In the present paper, we define two directed pseudo graphs. Then, we investigate the adjacency matrices of the defined graphs and show that the permanents of the adjacency matrices are Jacobsthal and Jacobsthal-Lucas numbers.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Graph Labeling and Dimension Problems · Advanced Mathematical Theories