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On the eccentricity matrices of line graphs of trees and wheel graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 مهر 1405 اصل مقاله (461.16 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31683.2927 | ||
| نویسنده | ||
| Shivani Chauhan* | ||
| Department of Applied Sciences and Humanities, ABES Engineering College, Ghaziabad, India-201009 | ||
| چکیده | ||
| The eccentricity matrix $\mathcal{E}(X)$ of a connected graph $X$ is obtained from the distance matrix of $X$ by keeping the largest nonzero entries in each row and each column, and leaving zeros in the remaining ones. In this paper, we investigate the spectral properties of the eccentricity matrices of line graphs of trees and wheel graphs. We prove that if $X$ is a tree on $n$ vertices of odd diameter $d \geq 5$, then the inertia of $\mathcal{E}(L(X))$ is $(2, 2, n-5)$. Furthermore, for trees of even diameter $d\geq 4$, we show that the inertia is $(l, l, n-2l-1)$, where $l$ denotes the number of diametrically distinguished vertices of $X$. Finally, we extend our analysis to determine the inertia, eigenvalues, and determinant of the eccentricity matrix for the line graphs of wheel graphs. We also relate its spectrum to the Dirichlet kernel. | ||
| کلیدواژه‌ها | ||
| Tree؛ line graph؛ eccentricity matrix | ||
| مراجع | ||
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