Vol. 24 No. 1 (2025): Mapana Journal of Sciences
Research Articles

Degree-Eccentricity Matrix of Graphs and Some Properties

  • Akhil B.,
  • Manju V. N.,
  • Roy John
Akhil B.
Department of Mathematics, University of Kerala, Kariavattom, Thiruvananthapuram, 695581, Kerala, India
Manju V. N.
Department of Mathematics, University of Kerala, Kariavattom, Thiruvananthapuram, 695581, Kerala, India.
Roy John
Department of Mathematics, St Stephen's College, Pathanapuram, Kollam - 689695, Kerala, India
DOI: https://doi.org/10.12723/mjs.72.7

Published 2025-04-05

Keywords

  • Degree-Eccentricity matrix,
  • Degree-Eccentricity energy,
  • Irreducibility,
  • Primitivity

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Abstract

This paper presents a new matrix for a given graph called the Degree-Eccentricity (DE) matrix, which consists of the degree and eccentricity of a vertex. Properties such as irreducibility and primitivity of this matrix are discussed. Further, we obtain the spectrum and energy of DE matrices associated with various classes of graphs and some graphs obtained through graph operations. Also, we try to develop an algorithm to construct a new class of graph with DE energy equal to
one. Further, we made an attempt to discover a few graphs with DE energy equal to one. Also, an upper bound for the eigenvalues of the DE matrix is discovered.

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