Extremal Values on the Kirchhoff Index of the Line Graph of Unicyclic Networks
Circuits, Systems, and Signal Processing, ISSN: 1531-5878
2024
Metric Options: CountsSelecting the 1-year or 3-year option will change the metrics count to percentiles, illustrating how an article or review compares to other articles or reviews within the selected time period in the same journal. Selecting the 1-year option compares the metrics against other articles/reviews that were also published in the same calendar year. Selecting the 3-year option compares the metrics against other articles/reviews that were also published in the same calendar year plus the two years prior.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Article Description
Let G be a simple connected graph with vertex set V(G) and edge set E(G). Suppose N represents a network derived from G by substituting a 1-ohm resistor for each edge of G. In that case, the resistance between u,v∈V(G) is analogous to the resistance between two equivalent nodes in network N. The Kirchhoff index of G is the summation of the resistance distances between all pairs of vertices in G. The line graph LG of G is a graph whose vertices correspond to the edges of G, and any two vertices of LG are adjacent if and only if the corresponding edges of G are incident with the same vertex of G. A unicyclic graph is a connected graph containing exactly one cycle. In this paper, we will identify the extremal values and unicyclic graphs for the Kirchhoff index of the line graph of unicyclic graphs by utilizing techniques derived from electrical networks.
Bibliographic Details
Springer Science and Business Media LLC
Provide Feedback
Have ideas for a new metric? Would you like to see something else here?Let us know