IRMA-International.org: Creator of Knowledge
Information Resources Management Association
Advancing the Concepts & Practices of Information Resources Management in Modern Organizations

The Hyper-Zagreb Index and Some Properties of Graphs

The Hyper-Zagreb Index and Some Properties of Graphs
View Sample PDF
Author(s): Rao Li (University of South Carolina at Aiken, USA)
Copyright: 2020
Pages: 15
Source title: Handbook of Research on Advanced Applications of Graph Theory in Modern Society
Source Author(s)/Editor(s): Madhumangal Pal (Vidyasagar University, India), Sovan Samanta (Tamralipta Mahavidyalaya, India)and Anita Pal (National Institute of Technology Durgapur, India)
DOI: 10.4018/978-1-5225-9380-5.ch006

Purchase

View The Hyper-Zagreb Index and Some Properties of Graphs on the publisher's website for pricing and purchasing information.

Abstract

Let G = (V(G), E(G)) be a graph. The complement of G is denoted by Gc. The forgotten topological index of G, denoted F(G), is defined as the sum of the cubes of the degrees of all the vertices in G. The second Zagreb index of G, denoted M2(G), is defined as the sum of the products of the degrees of pairs of adjacent vertices in G. A graph Gisk-Hamiltonian if for all X ⊂V(G) with|X| ≤ k, the subgraph induced byV(G) - Xis Hamiltonian. Clearly, G is 0-Hamiltonian if and only if G is Hamiltonian. A graph Gisk-path-coverableifV(G) can be covered bykor fewer vertex-disjoint paths. Using F(Gc) and M2(Gc), Li obtained several sufficient conditions for Hamiltonian and traceable graphs (Rao Li, Topological Indexes and Some Hamiltonian Properties of Graphs). In this chapter, the author presents sufficient conditions based upon F(Gc) and M2(Gc)for k-Hamiltonian, k-edge-Hamiltonian, k-path-coverable, k-connected, and k-edge-connected graphs.

Related Content

Vinod Kumar, Himanshu Prajapati, Sasikala Ponnusamy. © 2023. 18 pages.
Sougatamoy Biswas. © 2023. 14 pages.
Ganga Devi S. V. S.. © 2023. 10 pages.
Gotam Singh Lalotra, Ashok Sharma, Barun Kumar Bhatti, Suresh Singh. © 2023. 15 pages.
Nimish Kumar, Himanshu Verma, Yogesh Kumar Sharma. © 2023. 16 pages.
R. Soujanya, Ravi Mohan Sharma, Manish Manish Maheshwari, Divya Prakash Shrivastava. © 2023. 12 pages.
Nimish Kumar, Himanshu Verma, Yogesh Kumar Sharma. © 2023. 22 pages.
Body Bottom