Degree-based topological indices of double graphs and strong double graphs

The topological indices are useful tools to the theoretical chemists that are provided by the graph theory. They correlate certain physicochemical properties such as boiling point, strain energy, stability, etc. of chemical compounds. For a graph G, the double graph D[G] is a graph obtained by taking two copies of graph G and joining each vertex in one copy with the neighbors of corresponding vertex in another copy and strong double graph SD[G] of the graph G is the graph obtained by taking two copies of the graph G and joining each vertex v in one copy with the closed neighborhood of the corresponding vertex in another copy. In this paper, we compute the general sum-connectivity index, general Randic index, geometric–arithmetic index, general first Zagreb index, first and second multiplicative Zagreb indices for double graphs and strong double graphs and derive the exact expressions for these degree-base topological indices for double graphs and strong double graphs in terms of corresponding index of original graph G.

[1]  Bo Zhou,et al.  On general sum-connectivity index , 2010 .

[2]  Bo Zhou,et al.  On a novel connectivity index , 2009 .

[3]  Nilanjan De,et al.  F-Index of some graph operations , 2015, Discret. Math. Algorithms Appl..

[4]  Sakander Hayat,et al.  Computation of topological indices of certain networks , 2014, Appl. Math. Comput..

[5]  D. Vukicevic,et al.  Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges , 2009 .

[6]  Ali Reza Ashrafi,et al.  The first and second Zagreb indices of some graph operations , 2009, Discret. Appl. Math..

[7]  H. A. Ganie,et al.  Energy, Laplacian energy of double graphs and new families of equienergetic graphs , 2013, 1310.3204.

[8]  W. Imrich,et al.  Product Graphs: Structure and Recognition , 2000 .

[9]  M. Randic.  Characterization of molecular branching , 1975 .

[10]  I. Gutman,et al.  Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons , 1972 .

[11]  Ali Iranmanesh,et al.  Some inequalities for the multiplicative sum Zagreb index of graph operations , 2015 .

[12]  Muge Togan,et al.  The multiplicative Zagreb indices of graph operations , 2013 .

[13]  Spectra, Energy and Laplacian Energy of Strong Double Graphs , 2015 .

[14]  Norma Zagaglia Salvi,et al.  Double graphs , 2008, Discret. Math..

[15]  Martin Baca,et al.  On topological indices of fullerenes , 2015, Appl. Math. Comput..

[16]  Ali Reza Ashrafi,et al.  The Zagreb coindices of graph operations , 2010, Discret. Appl. Math..

[17]  N. Trinajstic,et al.  The Zagreb Indices 30 Years After , 2003 .

[18]  Sakander Hayat,et al.  Computation of Certain Topological Indices of Nanotubes Covered by C 5 and C 7 , 2015 .

[19]  Consonni,et al.  New Local Vertex Invariants and Molecular Descriptors Based on Functions of the Vertex Degrees , 2010 .

[20]  Sakander Hayat,et al.  On topological indices of certain interconnection networks , 2014, Appl. Math. Comput..

[21]  Ali Reza Ashrafi,et al.  The Szeged, vertex PI, first and second Zagreb indices of corona product of graphs , 2012 .

[22]  Sakander Hayat,et al.  On Degree Based Topological Indices of Certain Nanotubes , 2015 .