On path energy of graphs

On path energy of graphs. / Akbari, Saieed; Ghodrati, Amir Hossein; Gutman, Ivan et al.

In: Match, Vol. 81, No. 2, 01.01.2019, p. 465-470.

Research output: Contribution to journal › Article › peer-review

Akbari, S, Ghodrati, AH, Gutman, I, Hosseinzadeh, MA & Konstantinova, EV 2019, 'On path energy of graphs', Match, vol. 81, no. 2, pp. 465-470.

Akbari, S., Ghodrati, A. H., Gutman, I., Hosseinzadeh, M. A., & Konstantinova, E. V. (2019). On path energy of graphs. Match, 81(2), 465-470.

Akbari S, Ghodrati AH, Gutman I, Hosseinzadeh MA, Konstantinova EV. On path energy of graphs. Match. 2019 Jan 1;81(2):465-470.

Akbari, Saieed ; Ghodrati, Amir Hossein ; Gutman, Ivan et al. / On path energy of graphs. In: Match. 2019 ; Vol. 81, No. 2. pp. 465-470.

@article{58dbca0f0af540358d246da2598330d1,

title = "On path energy of graphs",

abstract = " For a graph G with vertex set {v1, . . ., v n }, let P(G) be an n × n matrix whose (i, j)-entry is the maximum number of internally disjoint viv j -paths in G, if i ≠ j, and zero otherwise. The sum of absolute values of the eigenvalues of P(G) is called the path energy of G, denoted by PE. We prove that PE of a connected graph G of order n is at least 2(n− 1) and equality holds if and only if G is a tree. Also, we determine PE of a unicyclic graph of order n and girth k, showing that for every n, PE is an increasing function of k. Therefore, among unicyclic graphs of order n, the maximum and minimum PE-values are for k = n and k = 3, respectively. These results give affirmative answers to some conjectures proposed in MATCH. ",

author = "Saieed Akbari and Ghodrati, {Amir Hossein} and Ivan Gutman and Hosseinzadeh, {Mohammad Ali} and Konstantinova, {Elena V.}",

year = "2019",

month = jan,

day = "1",

language = "English",

volume = "81",

pages = "465--470",

journal = "Match",

issn = "0340-6253",

publisher = "University of Kragujevac, Faculty of Science",

number = "2",

}

TY - JOUR

T1 - On path energy of graphs

AU - Akbari, Saieed

AU - Ghodrati, Amir Hossein

AU - Gutman, Ivan

AU - Hosseinzadeh, Mohammad Ali

AU - Konstantinova, Elena V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - For a graph G with vertex set {v1, . . ., v n }, let P(G) be an n × n matrix whose (i, j)-entry is the maximum number of internally disjoint viv j -paths in G, if i ≠ j, and zero otherwise. The sum of absolute values of the eigenvalues of P(G) is called the path energy of G, denoted by PE. We prove that PE of a connected graph G of order n is at least 2(n− 1) and equality holds if and only if G is a tree. Also, we determine PE of a unicyclic graph of order n and girth k, showing that for every n, PE is an increasing function of k. Therefore, among unicyclic graphs of order n, the maximum and minimum PE-values are for k = n and k = 3, respectively. These results give affirmative answers to some conjectures proposed in MATCH.

AB - For a graph G with vertex set {v1, . . ., v n }, let P(G) be an n × n matrix whose (i, j)-entry is the maximum number of internally disjoint viv j -paths in G, if i ≠ j, and zero otherwise. The sum of absolute values of the eigenvalues of P(G) is called the path energy of G, denoted by PE. We prove that PE of a connected graph G of order n is at least 2(n− 1) and equality holds if and only if G is a tree. Also, we determine PE of a unicyclic graph of order n and girth k, showing that for every n, PE is an increasing function of k. Therefore, among unicyclic graphs of order n, the maximum and minimum PE-values are for k = n and k = 3, respectively. These results give affirmative answers to some conjectures proposed in MATCH.

UR - http://www.scopus.com/inward/record.url?scp=85064385519&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85064385519

VL - 81

SP - 465

EP - 470

JO - Match

JF - Match

SN - 0340-6253

IS - 2

ER -

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