Extremal polyomino chains with respect to general Randić index

Bond incident degree (BID) indices of polyomino chains: A unified approach

“…The general Randić index R γ can be obtained from Equation (1.1) if one take θ a,b = (ab) γ where γ is non zero real number. Very recently, An and Xiong [4] derived an efficient formula (given in Corollary 2.8) to calculate the general Randić index of polyomino chains. Bearing in mind the fact…”

“…Corollary 2.8. [4] Let B n ∈ Ω n be a polyomino chain with n ≥ 3 squares and consisting of s segments S 1 , S 2 , S 3 , ..., S s with lengths l 1 , l 2 , ..., l s respectively. Let γ ≥ 1 be an arbitrary real number.…”

“…If at least one external segment of B + n has length 2, then no two internal segments with lengths 3 are consecutive. (4). If an external segment of B + n has length 3, then its adjacent segment has also length 3.…”

“…In [2,3], the same problem was addressed for some other BID indices. In this paper, an efficient closed form formula to calculate the BID indices of polyomino chains is given and by making use of this formula the extremal polyomino chains with respect to several BID indices are characterized, and thereby all the results reported in [4,7,34] and also some results of [3,25] are generalized.…”

Extremal pentagonal chains with respect to bond incident degree indices

“…The problem of characterizing the extremal 4-polygonal chains (also known as polyomino chains) with respect to BID indices, over the set of all polyomino chains with fixed number of squares, has attracted substantial attention from researchers in recent years. 21,[28][29][30][31][32] In this paper, we go one step further and attacked the aforementioned problem for the 5-polygonal chains (also known as pentagonal chains or pentachains). More precisely, we establish an efficient formula for calculating the BID indices of pentagonal chains.…”