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Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 4

THE REVISED EDGE SZEGED INDEX OF BRIDGE GRAPHS

Hui DONG
Bo ZHOU
Pages
559–566
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We give a formula for the revised edge Szeged index of a bridge graph, from which the revised edge Szeged indices for several classes of graphs are calculated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The revised edge Szeged index of a connected graph G is defined as Sz∗ e (G) = X e=uv∈E(G) mu(e|G) + m0(e|G) 2 mv(e|G) + m0(e|G) 2 , where E(G) is the edge set of G, mu(e|G) is the number of edges closer to vertex u than to vertex v in G, mv(e|G) is the number of edges closer to vertex v than to vertex u in G, and m0(e|G) is the number of edges equidistant from both ends of e.
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Key Findings & Data:The revised edge Szeged index of a connected graph G is defined as Sz∗ e (G) = X e=uv∈E(G) mu(e|G) + m0(e|G) 2 mv(e|G) + m0(e|G) 2 , where E(G) is the edge set of G, mu(e|G) is the number of edges closer to vertex u than to vertex v in G, mv(e|G) is the number of edges closer to vertex v than to vertex u in G, and m0(e|G) is the number of edges equidistant from both ends of e.
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Conclusion & Impact:We give a formula for the revised edge Szeged index of a bridge graph, from which the revised edge Szeged indices for several classes of graphs are calculated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Szeged index · Revised edge Szeged index · Revised Szeged index

Abstract

The revised edge Szeged index of a connected graph G is defined as Sz∗ e (G) = X e=uv∈E(G) mu(e|G) + m0(e|G) 2 mv(e|G) + m0(e|G) 2 , where E(G) is the edge set of G, mu(e|G) is the number of edges closer to vertex u than to vertex v in G, mv(e|G) is the number of edges closer to vertex v than to vertex u in G, and m0(e|G) is the number of edges equidistant from both ends of e. We give a formula for the revised edge Szeged index of a bridge graph, from which the revised edge Szeged indices for several classes of graphs are calculated.

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Cite This Article

DONG, H., ZHOU, B. (2022). THE REVISED EDGE SZEGED INDEX OF BRIDGE GRAPHS. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 4, 559–566. https://ajindex.com/articles/530532

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