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4121. The change of Seidel energy of Turán graph due to edge deletion

Invited abstract in session WC-29: Optimization issues on graphs I (Contributed), stream Combinatorial Optimization.

Wednesday, 12:30-14:00
Room: 157 (building: 208)

Authors (first author is the speaker)

1. Ayse Dilek Maden
Mathematics, Selcuk University
2. Şeyhmus Tarhan
3. Masood Ur Rehman
Physics and Mathematics, Anqing Normal University

Abstract

We consider any simple graph with finite vertex set and edge set.
Turán graph is defined as the complete r-partite graph formed by partitioning its vertex set into r subsets, with vertex number as equal as possible, and joining two vertices by an edge if and only if they are located in different subsets.In his paper, Haemers defined the Seidel energy of a graph as the sum of the absolute values of all Seidel eigenvalues of this graph. Heamers noticed that the Seidel energy of any graph is invariant when the Seidel switching and complement of that graph are taken. Tian showed complete bipartite graph and the empty graph are switching equivalent. Thus Seidel energies of empty graph, complete graph and complete graph with same order are the minimum among all graph of same order. Tian proved that the Seidel energy increases when an edge is deleted in the tripartite Turán graph, and then gave the problem of whether this property would be hold for all Turán graphs.
Liu and Chen, proved the above problem for quinate Turán graphs. We will show that the Seidel energy always increases when an edge is deleted for almost every Turán graphs.
W.H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem..
G.X. Tian, Y. Li, S.Y. Cui, The change of Seidel energy of tripartite Turán graph due to edge deletion, Linear Multilinear Algebra.
Y.Y. Liu and X. Chen, The change of Seidel energy of quinate Turán graph due to edge deletion. Discrete Applied Mathematics.

Keywords

Status: accepted

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