Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index

Guifu Su; Shuai Wang; Junfeng Du; Mingjing Gao; Kinkar Chandra Das; Yilun Shang

doi:10.3390/math10111802

Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index

Guifu Su, Shuai Wang, Junfeng Du, Mingjing Gao, Kinkar Chandra Das^*, Yilun Shang^*

^*Corresponding author for this work

Computer and Information Sciences Department

Research output: Contribution to journal › Article › peer-review

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Abstract

The forgotten topological index of a (molecule) graph is the sum of cubes of all its vertex degrees, which plays a significant role in measuring the branching of the carbon atom skeleton. It is meaningful and difficult to explore sufficient conditions for a given graph keeping certain properties in graph theory. In this paper, we mainly explore sufficient conditions in terms of the forgotten topological index for a graph to be ℓ-connected, ℓ-deficient, ℓ-Hamiltonian and ℓ−-independent, respectively. The conditions cannot be dropped.

Original language	English
Article number	1802
Number of pages	11
Journal	Mathematics
Volume	10
Issue number	11
DOIs	https://doi.org/10.3390/math10111802
Publication status	Published - 25 May 2022

Keywords

the forgotten topological index
ℓ -independent
ℓ-Hamiltonian
ℓ-connected
ℓ-deficient

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title = "Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index",

abstract = "The forgotten topological index of a (molecule) graph is the sum of cubes of all its vertex degrees, which plays a significant role in measuring the branching of the carbon atom skeleton. It is meaningful and difficult to explore sufficient conditions for a given graph keeping certain properties in graph theory. In this paper, we mainly explore sufficient conditions in terms of the forgotten topological index for a graph to be ℓ-connected, ℓ-deficient, ℓ-Hamiltonian and ℓ−-independent, respectively. The conditions cannot be dropped.",

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author = "Guifu Su and Shuai Wang and Junfeng Du and Mingjing Gao and Das, {Kinkar Chandra} and Yilun Shang",

note = "Funding information: G.S. is supported by the National Key Research and Development Project (2019YFB2006602) and Beijiing Natural Science Foundation of China (No.1222012). K.C.D. is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646).",

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AU - Su, Guifu

AU - Wang, Shuai

AU - Du, Junfeng

AU - Gao, Mingjing

AU - Das, Kinkar Chandra

AU - Shang, Yilun

N1 - Funding information: G.S. is supported by the National Key Research and Development Project (2019YFB2006602) and Beijiing Natural Science Foundation of China (No.1222012). K.C.D. is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646).

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N2 - The forgotten topological index of a (molecule) graph is the sum of cubes of all its vertex degrees, which plays a significant role in measuring the branching of the carbon atom skeleton. It is meaningful and difficult to explore sufficient conditions for a given graph keeping certain properties in graph theory. In this paper, we mainly explore sufficient conditions in terms of the forgotten topological index for a graph to be ℓ-connected, ℓ-deficient, ℓ-Hamiltonian and ℓ−-independent, respectively. The conditions cannot be dropped.

AB - The forgotten topological index of a (molecule) graph is the sum of cubes of all its vertex degrees, which plays a significant role in measuring the branching of the carbon atom skeleton. It is meaningful and difficult to explore sufficient conditions for a given graph keeping certain properties in graph theory. In this paper, we mainly explore sufficient conditions in terms of the forgotten topological index for a graph to be ℓ-connected, ℓ-deficient, ℓ-Hamiltonian and ℓ−-independent, respectively. The conditions cannot be dropped.

KW - the forgotten topological index

KW - ℓ -independent

KW - ℓ-Hamiltonian

KW - ℓ-connected

KW - ℓ-deficient

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ER -

Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index

Abstract

Keywords

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