Authors
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A. Alhevaz
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Author
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M. Baghipur
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Author
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H. A. Ganie
Department of School Education, JK Govt. Kashmir, India
Author
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K. C. Das
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
Author
Keywords:
Generalized distance matrix (spectrum), spectral radius, hypercube, unicyclic graph
Subjects:
05C50, 05C12, 15A18
Abstract
For a simple connected graph , the generalized distance matrix is defined as , . The largest eigenvalue of is called the generalized distance spectral radius or -spectral radius of . In this paper, we obtain some upper bounds for the generalized distance spectral radius in terms of various graph parameters associated with the structure of graph , and characterize the extremal graphs attaining these bounds. We determine the graphs with minimal generalized distance spectral radius among the trees with given diameter and among all unicyclic graphs with given girth. We also obtain the generalized distance spectrum of the square of the cycle and the square of the hypercube of dimension . We show that the square of the hypercube of dimension has three distinct generalized distance eigenvalues.