Unicyclic graphs with second largest and second smallest permanental sums

Tingzeng Wu and Wasin So

Applied Mathematics and Computation, 2019, vol. 351, issue C, 168-175

Abstract: Let A(G) be an adjacency matrix of a graph G. Then the polynomial π(G,x)=per(xI−A(G)) is called the permanental polynomial of G, and the permanental sum of G is the sum of the absolute values of the coefficients of π(G, x). In this paper, the second largest and second smallest permanental sums among connected unicyclic graphs and the corresponding extremal graphs are determined. In addition, we show that the computation of permanental sum is #P-complete.

Keywords: Complexity; Permanent; Permanental polynomial; Permanental sum; Unicyclic graph (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:351:y:2019:i:c:p:168-175

DOI: 10.1016/j.amc.2019.01.056

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