The IRMA Community
Newsletters
Research IRM
Click a keyword to search titles using our InfoSciOnDemand powered search:

The HyperZagreb Index and Some Properties of Graphs
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 GiskHamiltonian if for all X ⊂V(G) withX ≤ k, the subgraph induced byV(G)  Xis Hamiltonian. Clearly, G is 0Hamiltonian if and only if G is Hamiltonian. A graph GiskpathcoverableifV(G) can be covered bykor fewer vertexdisjoint 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 kHamiltonian, kedgeHamiltonian, kpathcoverable, kconnected, and kedgeconnected 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.


