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Graphs cospectral with a friendship graph or its complement | ||
| Transactions on Combinatorics | ||
| مقاله 4، دوره 2، شماره 4، اسفند 2013، صفحه 37-52 اصل مقاله (394.16 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2013.3621 | ||
| نویسندگان | ||
| Alireza Abdollahi* ؛ Shahrooz Janbaz؛ Mohammad Reza Oboudi | ||
| University of Isfahan | ||
| چکیده | ||
| Let $n$ be any positive integer and $F_n$ be the friendship (or Dutch windmill) graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $G\cong F_n$. Moreover if $G$ is connected and planar then $G\cong F_n$. All but one of connected components of $G$ are isomorphic to $K_2$. The complement $\overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $\overline{F_n}$ is cospectral with a graph $H$, then $H\cong \overline{F_n}$. | ||
| کلیدواژهها | ||
| Friendship graphs؛ cospectral graphs؛ adjacency eigenvalues | ||
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