Some Vertex-Degree-Based Topological Indices of Polyomino Chains

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

“…Then using this formula, we have derived some extremal results for BID indices of polyomino chains and hence obtained some corollaries for several well known BID indices: first and second Zagreb indices, first geometric-arithmetic index, Randić index, sum-connectivity index, harmonic index, multiplicative sum Zagreb index, second multiplicative Zagreb index, general Randić index R γ (for γ > 0), general atom-bond connectivity index ABC γ (for γ > 1) and general sum-connectivity index χ γ (for γ > 0). Thereby, we have generalized all the results of [4,7,34] and some of [3,25]. Moreover, we have showed that the linear chain L n and zigzag chain Z n has the minimum augmented Zagreb index and maximum atom-bond connectivity index, respectively, over the collection of all polyomino chains with n ≥ 3 squares.…”

“…Rada [25] recently proved that the linear chain has the extremal value for many well known BID indices. 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.…”

Total Independent Set Numbers on Catacondensed Polyomino Systems

“…If any four cells in G do not have a common vertex, then G is called the catacondensed or treelike polyomino system. The research on the catacondensed polyomino system is mostly focused on the path-like polyomino system so far, in which its central line forms a path [5][6][8][9]. In this paper, we consider the general catacondensed polyomino system, which is a chain polyomino system and its central line forms a tree.…”

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.…”