Zagreb indices of graphs with added edges
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Edge deletion and addition to a graph is an important combinatorial method in Graph Theory which enables one to calculate some properties of a graph by means of similar graphs. In this paper, as a sequel to a recent paper on edge deletion, we consider the change in the first and second Zagreb indices of a simple graph G when an arbitrary edge is added. This can be used to calculate the first and second Zagreb indices of larger graphs in terms of the Zagreb indices of smaller graphs. As some examples, some inequalities for the change of Zagreb indices for path, cycle, star, complete, complete bipartite and tadpole graphs are given.
Abstract
Edge deletion and addition to a graph is an important combinatorial method in Graph Theory which enables one to calculate some properties of a graph by means of similar graphs. In this paper, as a sequel to a recent paper on edge deletion, we consider the change in the first and second Zagreb indices of a simple graph G when an arbitrary edge is added. This can be used to calculate the first and second Zagreb indices of larger graphs in terms of the Zagreb indices of smaller graphs. As some examples, some inequalities for the change of Zagreb indices for path, cycle, star, complete, complete bipartite and tadpole graphs are given.
참고문헌 (10)
- K. Ch. Das, "On the first Zagreb index and multiplicative Zagreb coindices of graphs", Analele Stiintifice ale Universitatii Ovidius Constanta, 24(1) (2016)
- K. Ch. Das, "The multiplicative Zagreb indices of graph operations", Journal of Inequalities and Applications, 90, pp.1~14 (2013)
- I. Gutman, "Graph theory and molecular orbitals III, Total <TEX>${\pi}$<", TEX>-electron energy of alternant hydrocarbons, 1972, pp.17, 535~538
- M. H. Khalifeh, "The First and second Zagreb indices of some graph operations", Discrete Appl. Math., 157, pp.804~811 (2009)[DOI]
- V. Lokesha, "Computing ABC, GA, Randic and Zagreb Indices", Enlightments of Pure and Applied Mathematics(EPAM), 1(1), pp.17~28 (2015)
- P. S. Ranjini, "On the Zagreb indices of the line graphs of the subdivision graphs", Appl. Math. Comput., 218, pp.699~702 (2011)
- P. S. Ranjini, "On Zagreb Indices of the Sub-division Graphs", Int. J. of Math. Sci. & Eng. Appns (IJMSEA), 4, pp.221~228 (2010)
- M. Togan, "Some formulae and inequalities on several Zagreb indices of r-subdivision graphs", Enlightments of Pure and Applied Mathematics (EPAM), 1(1), pp.29~45 (2015)
- Muge TOGAN, "All versions of Zagreb indices and coindices of subdivision graphs of certain graph types", Advanced Studies in Contemporary Mathematics, 26(1), pp.227~236 (2016), 장전수학회
- A. Yurttas, "Zagreb indices of graphs with deleted edges"