About the Randić Connectivity, Modify Randić Connectivity and Sum-connectivity Indices of Titania Nanotubes TiO2(m,n)

Abstract

The Randi} Connectivity Index R(G) is one of the oldest connectivity index, introduced by Randi} in 1975. Another connectivity indices is the Sum-Connectivity Index X(G) introduced in 2008 by Zhou and Trinajsti}. Recently in 2011, a modification of the Randi} Connectivity Index of a graph G was introduced by Dvorak et al. In this paper, we compute these connectivity topological indices for a family of molecular graphs known as titania nanotubes TiO 2 (m,n).

Computing Sanskruti Index of Titania Nanotubes

“…T iO 2 sheets with a thickness of a few atomic layers were found to be remarkably stable [12]. Recently Malik and Imran [13] and some others researchers computed multiple Zagreb index of T iO 2 nanotubes, readers can see the paper series [14,15,16,17,18,19,20,21,22,23,24,25,26,27]. The graph of the Titania nanotube T iO 2 [m, n] is presented in Fig.…”

On the Atom Bond Connectivity Index of Titania Nanotubes TiO2 (m, n)

“…By using the edge partition, the graph has 2mn+4n+4 atoms of degree two, 2n atoms of degree four, 2mn atoms with degree five and the atoms of degree three are 2mn+4m. For more information and details see [14][15][16][17][18][19][20][21][22][23][24][25][26][27] In case the orthogonal cuts C i (i=1,…,2(n+1), see Figure-2: The values C i are classified as following:…”

On the Graphs of Minimum Degree At Least 3 Having Minimum Sum‐Connectivity Index

“…In the previous studies [10][11][12], the sum-connectivity index of several graphs of molecules was calculated. In [13], relation between the sum-connectivity index and average distance was established.…”