Energy of graphs with self-loops

Gutman, I.; Redžepović, Izudin; Furtula, Boris; Sahal, Ali Mohammed

doi:10.46793/match.87-3.645g

Cited by 34 publications

(50 citation statements)

References 10 publications

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“…2) At the second level, all eight vertices of CCS [1] are connected to different cubes through edges (bridge edges), which results in the construction of CCS [2] as depicted in Figure 2. 3) Again, at the next level, all the 7 × 8 vertices of degree 3 of CCS [2] are connected to distinct cubes through edges (bridge edges), which results in the construction of CCS [3] as depicted in Figure 3. 4) Similarly, we construct CCS[m] by affixing fresh cubes to the vertices of degree 3 at the preceding level.…”

Section: Crystal Cubic Carbon Structure Ccs[m]mentioning

confidence: 99%

Multiplicative Topological Indices of the Crystal Cubic Carbon Structure

Sharma

Bhat

Lal

2023

Cryst. Res. Technol.

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Chemical graph theory assumes an imperative part in displaying and planning any chemical structure or chemical network. The molecular structure of a chemical molecule strongly relates to its properties. The graphs that make up the molecular structure are made up of units known as vertices, and the covalent bonds that connect them are known as edges. The topological indices of any chemical compound can be used to better understand the chemical structure and its biological characteristics. In this study, the degree-based multiplicative topological indices of the crystalline structure of cubic carbon (CCS) for levels m = 3-10 are computed, CCS[m] being one of the precious carbon allotropes.

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Section: Crystal Cubic Carbon Structure Ccs[m]mentioning

confidence: 99%

Multiplicative Topological Indices of the Crystal Cubic Carbon Structure

Sharma

Bhat

Lal

2023

Cryst. Res. Technol.

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“…Because of its importance and significance in chemistry, the energy E(G σ ) of G σ has been recently introduced in [7]:…”

Section: The Adjacency Matrixmentioning

confidence: 99%

On the Conjecture Related to the Energy of Graphs with Self–Loops

Jovanović¹,

Zogić²,

Glogic³

2022

MATCH

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Let Gσ be a graph obtained by attaching a self-loop, or just a loop, for short, at each of σ chosen vertices of a given graph G. Gutman et al. have recently introduced the concept of the energy of graphs with self-loops, and conjectured that the energy E(G) of a graph G of order n is always strictly less than the energy E(Gσ) of a corresponding graph Gσ, for 1 ≤ σ ≤ n − 1. In this paper, a simple set of graphs which disproves this conjecture is exposed, together with some remarks regarding the standard deviations of the (adjacency) eigenvalues of G and Gσ, respectively.

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“…Since graph with self-loops find its application in Chemistry, [8,9,13,14] Gutman et al defined adjacency matrix A(G S ) [6] of graph G S in 2021.…”

Section: Introductionmentioning

confidence: 99%

Laplacian Energy of a Graph with Self-Loops

Anchan¹,

D’Souza²,

Gowtham³

et al. 2023

match

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The purpose of this paper is to extend the concept of Laplacian energy from simple graph to a graph with self-loops. Let G be a simple graph of order n, size m and GS is the graph obtained from G by adding σ self-loops. We define Laplacian energy of GS aswhere µ1(GS), µ2(GS), . . . , µn(GS) are eigenvalues of the Laplacian matrix of GS. In this paper some basic proprties of Laplacian eigenvalues and bounds for Laplacian energy of GS are investigated. This paper is limited to bounds in analogy with bounds of E(G) and LE(G) but with some significant differences, more sharper bounds can be found.

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Energy of graphs with self-loops

Cited by 34 publications

References 10 publications

Multiplicative Topological Indices of the Crystal Cubic Carbon Structure

Multiplicative Topological Indices of the Crystal Cubic Carbon Structure

On the Conjecture Related to the Energy of Graphs with Self–Loops

Laplacian Energy of a Graph with Self-Loops

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