Extremal polyomino chains with respect to general Randić index

Mingqiang An () and Liming Xiong
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Mingqiang An: Tianjin University of Science and Technology
Liming Xiong: Beijing Institute of Technology

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 10, 635-647

Abstract: Abstract For a (molecular) graph $$G,$$ G , the general Randić index $$R_{\alpha }(G)$$ R α ( G ) is defined as the sum of the weights $$[d_{u}d_{v}]^{\alpha }$$ [ d u d v ] α of all edges $$uv$$ u v of $$G,$$ G , where $$d_{u}$$ d u (or $$d_{v}$$ d v ) denotes the degree of a vertex $$u$$ u (or $$v$$ v ) in $$G$$ G and $$\alpha $$ α is an arbitrary real number. In this paper, we give an efficient formula for computing the general Randić index of polyomino chains and characterize the extremal polyomino chains with respect to this index, which generalizes one of the main results in (Yarahmadi et al. Appl Math Lett 25:166–171, 2012).

Keywords: General Randić index; Polyomino chain; Extremal graphs; Degree (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9781-6

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