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Advances on Fixed Point Results on Partial Metric Spaces Read chapter Read first chapter

2019 | OriginalPaper | Chapter

9. Effect of Edge Deletion and Addition on Zagreb Indices of Graphs

Authors : Muge Togan, Aysun Yurttas, Ahmet Sinan Cevik, Ismail Naci Cangul

Published in: Mathematical Methods in Engineering

Publisher: Springer International Publishing

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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. The effect of edge addition on the first and second Zagreb indices was recently investigated by the authors. In this sequel paper, we consider the change in the first and second Zagreb indices of any simple graph G when an arbitrary edge is deleted. Further, we calculate the change in the first Zagreb index when an arbitrary number of edges are deleted. This method 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, we give some inequalities for the change of Zagreb indices for path, cycle, star, complete, complete bipartite, and tadpole graphs.

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previous chapter Comparison on Solving a Class of Nonlinear Systems of Partial Differential Equations and Multiple Solutions of Second Order Differential Equations
next chapter The Limit q-Bernstein Operators with Varying q
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Metadata
Title
Effect of Edge Deletion and Addition on Zagreb Indices of Graphs
Authors
Muge Togan
Aysun Yurttas
Ahmet Sinan Cevik
Ismail Naci Cangul
Copyright Year
2019
Book
Mathematical Methods in Engineering

Print ISBN: 978-3-319-91064-2

Electronic ISBN: 978-3-319-91065-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-91065-9_9

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