On symmetric division deg index of unicyclic graphs and bicyclic graphs with given matching number

Sun, Xiaoling; Gao, Yubin; Du, Jianwei

doi:10.3934/math.2021523

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…G (2) G (3) n − 8 ≥ 0 G (4) n − 8 ≥ 0 G (5) n − 10 ≥ 0 G (6) Figure 3: All possible pentacyclic graphs of order n and maximum degree n − 1.…”

Section: Discussionmentioning

confidence: 99%

“…In order to check the chemical applicability of the SDD index, Furtula et al [4] conducted a thorough multidimensional investigation of the SDD index and discovered that it is a practicable and feasible topological index that outperforms a number of other indices of a similar kind. Ali et al and Sun et al [5,6] provide information on certain extremal results concerning the SDD index. e papers [7,15] may be consulted for di erent bounds on the SDD index.…”

Section: Introductionmentioning

confidence: 99%

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On the Maximum Symmetric Division Deg Index of k‐Cyclic Graphs

Albalahi

Ali

2022

Journal of Mathematics

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Let G be a graph. Denote by d u , the degree of a vertex u of G and represent by v w , the edge of G with the end-vertices v and w . The sum of the quantities d u 2 + d v 2 d u − 1 d u − 1 over all edges u v of G is known as the symmetric division deg (SDD) index of G . A connected graph with n vertices and n − 1 + k edges is known as a (connected) k -cyclic graph. One of the results proved in this study is that the graph possessing the largest SDD index over the class of all connected k -cyclic graphs of a fixed order n must have the maximum degree n − 1 . By utilizing this result, the graphs attaining the largest SDD index over the aforementioned class of graphs are determined for every k = 0,1 , … , 5 . Although, the deduced results, for k = 0,1,2 , are already known, however, they are proved here in a shorter and an alternative way. Also, the deduced results, for k = 3,4,5 , are new, and they provide answers to two open questions posed in the literature.

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“…G (2) G (3) n − 8 ≥ 0 G (4) n − 8 ≥ 0 G (5) n − 10 ≥ 0 G (6) Figure 3: All possible pentacyclic graphs of order n and maximum degree n − 1.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Maximum Symmetric Division Deg Index of k‐Cyclic Graphs

Albalahi

Ali

2022

Journal of Mathematics

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“…The graphs attaining the maximum SDD index among all n-order trees with a fixed matching number (and hence with a fixed independence number; because the addition of the matching number and the independence number of every n-order bipartite graph is n) were also found in [23]. Also, in [75], the graphs having the maximum SDD index were characterized over the classes of all (i) connected unicyclic graphs possessing perfect matching (ii) connected bicyclic graphs possessing perfect matching (iii) n-order connected unicyclic graphs with a fixed matching number (iv) n-order connected bicyclic graphs with a fixed matching number. Recently, the problem of finding the graphs attaining the first five minimum values of the SDD index among all connected bicyclic graphs possessing perfect matching was attacked in [71].…”

Section: Conjecture 2 [1]mentioning

confidence: 93%

Symmetric Division Deg Index: Extremal Results and Bounds

Ali¹,

Gutman²,

Redžepović³

et al. 2023

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Existing studies show that the symmetric division deg (SDD) index deserves to be treated as a useful and practicable molecular descriptor, preferable to some of the more widely used ones. The primary purpose of this review is to summarize the existing extremal results and bounds for the SDD index. Several open problems regarding the aforementioned index, arising from the known results, are also proposed.

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Sharp bounds on the symmetric division deg index of graphs and line graphs

Liu,

Huang

2023

Comp. Appl. Math.

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On symmetric division deg index of unicyclic graphs and bicyclic graphs with given matching number

Cited by 6 publications

References 8 publications

On the Maximum Symmetric Division Deg Index of k‐Cyclic Graphs

On the Maximum Symmetric Division Deg Index of k‐Cyclic Graphs

Symmetric Division Deg Index: Extremal Results and Bounds

Sharp bounds on the symmetric division deg index of graphs and line graphs

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