On Edge Mostar Index of Graphs

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LIU HECHAO; SONG LING; XIAO QIQI; Tang Zikai

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Journal: Iranian Journal of Mathematical Chemistry Year:2020 | Volume:11 | Issue:2 Page(s): 95-106

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Information Journal Paper

Title

On Edge Mostar Index of Graphs

Author(s)

LIU HECHAO | SONG LING | XIAO QIQI | Tang Zikai | Issue Writer Certificate

Keywords

Edge Mostar index

Tree

Unicyclic graph

Cacti

Extremal value

Abstract

The Edge Mostar index 𝑀 𝑜 𝑒 (𝐺 ) of a connected graph 𝐺 is defined as 𝑀 𝑜 𝑒 (𝐺 )=Σ 𝑒 =𝑢 𝑣 ∈ 𝐸 (𝐺 ) |𝑚 𝑢 (𝑒 |𝐺 )− 𝑚 𝑣 (𝑒 |𝐺 )|, where 𝑚 𝑢 (𝑒 |𝐺 )and 𝑚 𝑣 (𝑒 |𝐺 ) are, respectively, the number of edges of 𝐺 lying closer to vertex 𝑢 than to vertex 𝑣 and the number of edges of 𝐺 lying closer to vertex 𝑣 than to vertex 𝑢 . In this paper, we determine the Extremal values of Edge Mostar index of some graphs. We characterize extremal Trees, Unicyclic graphs and determine the extremal graphs with maximum and second maximum Edge Mostar index among Cacti with size 𝑚 and 𝑡 cycles. At last, we give some open problems.

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APA: Copy

LIU, HECHAO, SONG, LING, XIAO, QIQI, & Tang, Zikai. (2020). On Edge Mostar Index of Graphs. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 11(2), 95-106. SID. https://sid.ir/paper/654553/en

Vancouver: Copy

LIU HECHAO, SONG LING, XIAO QIQI, Tang Zikai. On Edge Mostar Index of Graphs. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY[Internet]. 2020;11(2):95-106. Available from: https://sid.ir/paper/654553/en

IEEE: Copy

HECHAO LIU, LING SONG, QIQI XIAO, and Zikai Tang, “On Edge Mostar Index of Graphs,” IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, vol. 11, no. 2, pp. 95–106, 2020, [Online]. Available: https://sid.ir/paper/654553/en

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