Unicyclic graphs with maximal energy

Hou, Yaoping; Gutman, Iván; Woo, Ching-Wah

doi:10.1016/s0024-3795(01)00609-7

Cited by 54 publications

(21 citation statements)

References 6 publications

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“…1.1. This conjecture was proved to be true for m = n − 1, 2(n − 2) by Caporossi et al ([5], Theorem 1), and m = n by Hou [17]. In [22], Li, Zhang and Wang confirmed this conjecture for bipartite graphs.…”

Section: Introductionmentioning

confidence: 84%

On oriented graphs with minimal skew energy

Gong

2014

ELA

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Let S(G σ ) be the skew-adjacency matrix of an oriented graph G σ . The skew energy of G σ is defined as the sum of all singular values of its skewadjacency matrix S(G σ ). In this paper, we first deduce an integral formula for the skew energy of an oriented graph. Then we determine all oriented graphs with minimal skew energy among all connected oriented graphs on n vertices with m (n ≤ m < 2(n − 2)) arcs, which is an analogy to the conjecture for the energy of undirected graphs proposed by Caporossi et al.[G. Caporossi, D. Cvetković, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs. 2. Finding graphs with external energy, J. Chem. Inf. Comput. Sci. 39 (1999) 984-996.].

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Section: Introductionmentioning

confidence: 84%

On oriented graphs with minimal skew energy

Gong

2014

ELA

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“…, and b 2 (G) equals the number of edges of G. For unicyclic graphs or bipartite graphs, it can be shown [10,11] that…”

Section: Preliminariesmentioning

confidence: 99%

On the minimal energy of conjugated unicyclic graphs with maximum degree at most 3

Bai

Ji³

2015

Discrete Applied Mathematics

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The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. Let n be an even number and U n be the set of all conjugated unicyclic graphs of order n with maximum degree at most 3. Let S n ≇ G ∈ U n and the girth of G is not divisible by 4, then E(G) > E(S n 2 n ). Let A n be the unicyclic graph obtained by attaching a 4-cycle to one of the two leaf vertices of the path P n 2 −1 and a pendent edge to each other vertices of P n 2 −1 . In this paper, we prove that A n is the unique unicyclic graph in U n with minimal energy.

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“…The reader is referred to [3][4][5]11] for a comprehensive study on the bounds for the energy of bipartite graphs, trees and benzenoids. Hou [6] addressed the problem of finding the uncyclic graphs with minimal energy. Hou et al [7] considered the problem of finding unicyclic graphs with maximal energy.…”

Section: Introductionmentioning

confidence: 99%

“…Hou [6] addressed the problem of finding the uncyclic graphs with minimal energy. Hou et al [7] considered the problem of finding unicyclic graphs with maximal energy. They find unicyclic graphs with maximum energy among all unicyclic graphs with fixed number of vertices and with fixed length of cycles.…”

Section: Introductionmentioning

confidence: 99%

Extremal energy of digraphs with two linear subdigraphs

Farooq¹,

Khan²,

Masood³

2016

Kragujevac J Math

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Abstract. The eigenvalues of a digraph are the eigenvalues of its adjacency matrix. The sum of the absolute values of the real part of the eigenvalues is called the energy of the digraph. The extremal energy of bicyclic digraphs with vertex-disjoint directed cycles is known. In this paper, we consider a class of bicyclic digraphs with exactly two linear subdigraphs of equal length. We find the minimal and maximal energy among the digraphs in this class.

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Unicyclic graphs with maximal energy

Cited by 54 publications

References 6 publications

On oriented graphs with minimal skew energy

On oriented graphs with minimal skew energy

On the minimal energy of conjugated unicyclic graphs with maximum degree at most 3

Extremal energy of digraphs with two linear subdigraphs

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