**Title:** Euclidean Degree Energy Graphs

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-20-00030; **Volume 3 / Issue 1 / Year 2021**, Pages 89-105

**Document Type:** Research Paper

**Author(s):** Yate Shanthakumari ^{a} , Mariswamy Smitha ^{b} , Veerabadhraiah Lokesha ^{c}

^{a}Department of Studies in Mathematics, Vijayanagara Sri krishnadevaraya University, Ballari, Karnataka, India

^{b}Department of Mathematics, JSS Science and Technology University, Mysuru-570 006, India

^{c}Department of Studies in Mathematics, Vijayanagara Sri krishnadevaraya University, Ballari, Karnataka, India

Received: 18 September 2020, Accepted: 15 December 2020, Available online: 7 January 2021.

**Corresponding Author:** Mariswamy Smitha (Email address: smitham@jssstuniv.in)

**Full Text:** PDF

**Abstract**

In this paper we introduce new energy of graph that is Euclidean degree energy. We obtain characteristic polynomial of the Euclidean degree of standard graphs and graphs obtained by some graph operations and also we characterize Euclidean hyperenergetic, nonhyperenergetic and borderenergetic graphs.

**Keywords:** Euclidean degree matrix, Euclidean degree polynomial and energy, Hyperenergetic graphs

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