TY - JOUR
T1 - Computing the forgotten topological index of four operations on graphs
AU - Akhter, Shehnaz
AU - Imran, Muhammad
N1 - Publisher Copyright:
© 2016 Kalasalingam University
PY - 2017/4
Y1 - 2017/4
N2 - For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. The F-index of a graph G denoted by F(G) or M3(G) is defined as the sum of cubes of the degrees of vertices of the graph. The total π-electron energy depends on the degree based sum M1(G)=∑v∈VdegG(v)2 and F(G)=∑v∈VdegG(v)3, it was shown in the study of structure-dependency of total π-electron energy in 1972. The first index was named first Zagreb index and the second sum ∑v∈VdegG(v)3 has been never further studied. Recently, this sum was named Forgotten index or the F-index by Furtula and Gutman and it was shown to have an exceptional applicative potential. The first and second Zagreb indices for the four operations on graphs were studied by Deng et al. (2016). In this paper, we extend this study to the F-index of graphs and determine the closed formulas for the F-index of four operations on graphs.
AB - For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. The F-index of a graph G denoted by F(G) or M3(G) is defined as the sum of cubes of the degrees of vertices of the graph. The total π-electron energy depends on the degree based sum M1(G)=∑v∈VdegG(v)2 and F(G)=∑v∈VdegG(v)3, it was shown in the study of structure-dependency of total π-electron energy in 1972. The first index was named first Zagreb index and the second sum ∑v∈VdegG(v)3 has been never further studied. Recently, this sum was named Forgotten index or the F-index by Furtula and Gutman and it was shown to have an exceptional applicative potential. The first and second Zagreb indices for the four operations on graphs were studied by Deng et al. (2016). In this paper, we extend this study to the F-index of graphs and determine the closed formulas for the F-index of four operations on graphs.
KW - Forgotten index
KW - Operations on graphs
KW - Subdivision of graph
KW - Total graph
KW - Zagreb index
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U2 - 10.1016/j.akcej.2016.11.012
DO - 10.1016/j.akcej.2016.11.012
M3 - Article
AN - SCOPUS:85009381987
SN - 0972-8600
VL - 14
SP - 70
EP - 79
JO - AKCE International Journal of Graphs and Combinatorics
JF - AKCE International Journal of Graphs and Combinatorics
IS - 1
ER -