Degree exponent sum energy of a graph

Basavanagoud, B.; Eshwarachandra, Chitra

doi:10.56947/gjom.v8i1.306

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…Definition 2.1. (Basavanagoud & Eshwarachandra, 2020) The DES matrix of order 𝒏 × 𝒏 associated with 𝜞 𝑮 [𝑿] is given by 𝑫𝑬𝑺(𝜞 𝑮 [𝑿]) = [𝒅𝒆𝒔 𝒑𝒒 ] whose (𝒑, 𝒒)-th entry is…”

Section: Preliminariesmentioning

confidence: 99%

Degree Exponent Sum Energy of Commuting Graph for Dihedral Groups

Romdhini

Nawawi²,

Yee³

2022

MJS

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For a finite group G and a nonempty subset X of G, we construct a graph with a set of vertex X such that any pair of distinct vertices of X are adjacent if they are commuting elements in G. This graph is known as the commuting graph of G on X, denoted by ΓG [X]. The degree exponent sum (DES) matrix of a graph is a square matrix whose (p,q)-th entry is is dvp dvq + dvqdvp whenever p is different from q, otherwise, it is zero, where dvp (or dvq ) is the degree of the vertex vp (or vertex, vq) of a graph. This study presents results for the DES energy of commuting graph for dihedral groups of order 2n, using the absolute eigenvalues of its DES matrix.

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Section: Preliminariesmentioning

confidence: 99%

Degree Exponent Sum Energy of Commuting Graph for Dihedral Groups

Romdhini

Nawawi²,

Yee³

2022

MJS

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“…where ψ(d i , d j ) is a function on the degrees of vertices v i and v j , while R(i, j) is the relation between the vertices v i and v j . The adjacency matrix A(G) of G is the most extensively studied such matrix [17], also the concepts of degree sum matrix [15], degree exponent matrix [16], degree exponent sum matrix [2], Harary matrix [14] etc., have also been proposed. Inspired by these previous works, we aim to present a new type of matrix known as the open neighborhood matrix ON M (G) of G, whose (i, j) th entry is…”

Section: Introductionmentioning

confidence: 99%

On open neighborhood energy of graphs

K A,

2023

GJOM

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The open neighborhood of a vertex u denoted by N(u) in a simple connected graph G is the collection of all vertices other than u and adjacent to u. In this paper, we introduce a square matrix of order n, called the open neighborhood matrix, ONM(G) of a graph G whose (i, j)th entry is |N(vi) ∩ N(vj)|/(di+dj) whenever vi~vj, i≠ j; and zero otherwise, where di and dj, are the degrees of vi and vj respectively. We then establish the relationship between the connectedness of the graph G and the multiplicity of the eigenvalue zero of the matrix ONM(G), if it exists. Furthermore, we found the bounds for the largest open neighbourhood eigenvalue and open neighbourhood energy of graphs.

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“…For detailed work, see [15][16][17][18]. Motivated by previous research related to degree and distance in a graph such as distance energy [1,2], degree sum energy [3,4], degree square sum polynomial [8], complementary distance energy [5], degree exponent energy [6,7], degree exponent sum energy [9], in order to upgrade, we now introduce the concept of degree sum distance energy of a connected graph. The purpose of this paper is to compute the characteristic polynomial, eigenvalues and energy of degree sum distance matrix of a graph.…”

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confidence: 99%