On the spectral reconstruction problem for digraphs
The idiosyncratic polynomial of a graph $G$ with adjacency matrix $A$ is the characteristic polynomial of the matrix $ A + y(J-A-I)$, where $I$ is the identity matrix and $J$ is the all-ones matrix. It follows from a theorem of Hagos (2000) combined with an earlier result of Johnson and Newman (1980...
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creator | Bankoussou-mabiala, Edward Boussaïri, Abderrahim Chaïchaâ, Abdelhak Chergui, Brahim Lakhlifi, Soufiane |
description | The idiosyncratic polynomial of a graph $G$ with adjacency matrix $A$ is the
characteristic polynomial of the matrix $ A + y(J-A-I)$, where $I$ is the
identity matrix and $J$ is the all-ones matrix. It follows from a theorem of
Hagos (2000) combined with an earlier result of Johnson and Newman (1980) that
the idiosyncratic polynomial of a graph is reconstructible from the multiset of
the idiosyncratic polynomial of its vertex-deleted subgraphs. For a digraph $G$
with adjacency matrix $A$, we define its idiosyncratic polynomial as the
characteristic polynomial of the matrix $ A + y(J-A-I)+zA^{T}$. By forbidding
two fixed digraphs on three vertices as induced subdigraphs, we prove that the
idiosyncratic polynomial of a digraph is reconstructible from the multiset of
the idiosyncratic polynomial of its induced subdigraphs on three vertices. As
an immediate consequence, the idiosyncratic polynomial of a tournament is
reconstructible from the collection of its $3$-cycles. Another consequence is
that all the transitive orientations of a comparability graph have the same
idiosyncratic polynomial. |
doi_str_mv | 10.48550/arxiv.1910.13914 |
format | Article |
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characteristic polynomial of the matrix $ A + y(J-A-I)$, where $I$ is the
identity matrix and $J$ is the all-ones matrix. It follows from a theorem of
Hagos (2000) combined with an earlier result of Johnson and Newman (1980) that
the idiosyncratic polynomial of a graph is reconstructible from the multiset of
the idiosyncratic polynomial of its vertex-deleted subgraphs. For a digraph $G$
with adjacency matrix $A$, we define its idiosyncratic polynomial as the
characteristic polynomial of the matrix $ A + y(J-A-I)+zA^{T}$. By forbidding
two fixed digraphs on three vertices as induced subdigraphs, we prove that the
idiosyncratic polynomial of a digraph is reconstructible from the multiset of
the idiosyncratic polynomial of its induced subdigraphs on three vertices. As
an immediate consequence, the idiosyncratic polynomial of a tournament is
reconstructible from the collection of its $3$-cycles. Another consequence is
that all the transitive orientations of a comparability graph have the same
idiosyncratic polynomial.</description><identifier>DOI: 10.48550/arxiv.1910.13914</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2019-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1910.13914$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1910.13914$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bankoussou-mabiala, Edward</creatorcontrib><creatorcontrib>Boussaïri, Abderrahim</creatorcontrib><creatorcontrib>Chaïchaâ, Abdelhak</creatorcontrib><creatorcontrib>Chergui, Brahim</creatorcontrib><creatorcontrib>Lakhlifi, Soufiane</creatorcontrib><title>On the spectral reconstruction problem for digraphs</title><description>The idiosyncratic polynomial of a graph $G$ with adjacency matrix $A$ is the
characteristic polynomial of the matrix $ A + y(J-A-I)$, where $I$ is the
identity matrix and $J$ is the all-ones matrix. It follows from a theorem of
Hagos (2000) combined with an earlier result of Johnson and Newman (1980) that
the idiosyncratic polynomial of a graph is reconstructible from the multiset of
the idiosyncratic polynomial of its vertex-deleted subgraphs. For a digraph $G$
with adjacency matrix $A$, we define its idiosyncratic polynomial as the
characteristic polynomial of the matrix $ A + y(J-A-I)+zA^{T}$. By forbidding
two fixed digraphs on three vertices as induced subdigraphs, we prove that the
idiosyncratic polynomial of a digraph is reconstructible from the multiset of
the idiosyncratic polynomial of its induced subdigraphs on three vertices. As
an immediate consequence, the idiosyncratic polynomial of a tournament is
reconstructible from the collection of its $3$-cycles. Another consequence is
that all the transitive orientations of a comparability graph have the same
idiosyncratic polynomial.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrFuwjAUhWEvDBX0ATrhFwjk2k4cjwhBWwmJAfboxr6GSCGJbgKib98WmI70D0efEB-QLkyRZekS-V7fFuD-AmgH5k3ofSvHM8mhJz8yNpLJd-0w8tWPddfKnruqoYuMHctQnxj78zATk4jNQO-vnYrDdnNcfyW7_ef3erVLMLcmyVKfWV1hHl1hdDBKO5MHogAVAipLlgA0FlY5slYZr1yk4FQEhUWKeirmz9cHuuy5viD_lP_48oHXvwr-Pv0</recordid><startdate>20191030</startdate><enddate>20191030</enddate><creator>Bankoussou-mabiala, Edward</creator><creator>Boussaïri, Abderrahim</creator><creator>Chaïchaâ, Abdelhak</creator><creator>Chergui, Brahim</creator><creator>Lakhlifi, Soufiane</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20191030</creationdate><title>On the spectral reconstruction problem for digraphs</title><author>Bankoussou-mabiala, Edward ; Boussaïri, Abderrahim ; Chaïchaâ, Abdelhak ; Chergui, Brahim ; Lakhlifi, Soufiane</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-50c573ba6f9843d423946deed1ba1a27e7e113a8729e7724c29fed92f12a80a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Bankoussou-mabiala, Edward</creatorcontrib><creatorcontrib>Boussaïri, Abderrahim</creatorcontrib><creatorcontrib>Chaïchaâ, Abdelhak</creatorcontrib><creatorcontrib>Chergui, Brahim</creatorcontrib><creatorcontrib>Lakhlifi, Soufiane</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bankoussou-mabiala, Edward</au><au>Boussaïri, Abderrahim</au><au>Chaïchaâ, Abdelhak</au><au>Chergui, Brahim</au><au>Lakhlifi, Soufiane</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the spectral reconstruction problem for digraphs</atitle><date>2019-10-30</date><risdate>2019</risdate><abstract>The idiosyncratic polynomial of a graph $G$ with adjacency matrix $A$ is the
characteristic polynomial of the matrix $ A + y(J-A-I)$, where $I$ is the
identity matrix and $J$ is the all-ones matrix. It follows from a theorem of
Hagos (2000) combined with an earlier result of Johnson and Newman (1980) that
the idiosyncratic polynomial of a graph is reconstructible from the multiset of
the idiosyncratic polynomial of its vertex-deleted subgraphs. For a digraph $G$
with adjacency matrix $A$, we define its idiosyncratic polynomial as the
characteristic polynomial of the matrix $ A + y(J-A-I)+zA^{T}$. By forbidding
two fixed digraphs on three vertices as induced subdigraphs, we prove that the
idiosyncratic polynomial of a digraph is reconstructible from the multiset of
the idiosyncratic polynomial of its induced subdigraphs on three vertices. As
an immediate consequence, the idiosyncratic polynomial of a tournament is
reconstructible from the collection of its $3$-cycles. Another consequence is
that all the transitive orientations of a comparability graph have the same
idiosyncratic polynomial.</abstract><doi>10.48550/arxiv.1910.13914</doi><oa>free_for_read</oa></addata></record> |
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subjects | Mathematics - Combinatorics |
title | On the spectral reconstruction problem for digraphs |
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