Document Zbl 0623.05038

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If the length of the cycle is fixed, extremal graphs in the first ordering are obtained by attaching a star and a path to a cycle. For the other ordering minimal graphs are not known. A table of the 89 unicyclic graphs on 8 vertices with their spectra is appended.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A4010560">Cited in <strong>43</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C50" title="MSC2020">05C50</a> </td> <td class="space"> Graphs and linear algebra (matrices, eigenvalues, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C35" title="MSC2020">05C35</a> </td> <td class="space"> Extremal problems in graph theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aordering">ordering</a>; <a href="/?q=ut%3Aunicyclic+graphs">unicyclic graphs</a>; <a href="/?q=ut%3Aspectral+moments">spectral moments</a>; <a href="/?q=ut%3Alargest+eigenvalue">largest eigenvalue</a>; <a href="/?q=ut%3Aextremal+graphs">extremal graphs</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0623.05038" data-ciurl="/ci/04010560" data-biburl="/bibtex/04010560.bib" data-amsurl="/amsrefs/04010560.bib" data-xmlurl="/xml/04010560.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/04010560.pdf" title="Zbl 0623.05038 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/BF01788525" aria-label="DOI for “Spectra of unicyclic graphs”" title="10.1007/BF01788525">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Baker, G.A.: Drum shapes and isospectral graphs. J. Math. Phys.7, 2238–2242 (1966) · <a href="/0203.27401" class="nowrap">Zbl 0203.27401</a> · <a href="https://doi.org/10.1063/1.1704911" class="nowrap">doi:10.1063/1.1704911</a></td> </tr><tr> <td>[2]</td> <td class="space">Bussemaker, F.C., Čobeljić, S., Cvetković, D.M., Seidel, J.J.: Computer investigation of cubic graphs (Technological University Eindhoven, T.H. Report 76-WSK-01, Cubic graphs on 14 vertices) J. Comb. Theory (B)23, 234–235 (1977) · <a href="/0369.05045" class="nowrap">Zbl 0369.05045</a> · <a href="https://doi.org/10.1016/0095-8956(77)90034-X" class="nowrap">doi:10.1016/0095-8956(77)90034-X</a></td> </tr><tr> <td>[3]</td> <td class="space">Cvetković, D.: A project for using computers in the further development of graph theory. In: Theory and Application of graphs (Proc. 4th Internat. Conf. on Theory and Appl. of Graphs, Kalamazoo 1980) edited by Chartrand, G., Alvai, Y., Goldsmith, D.L., Lesniak-Foster, L., Lick, D.R., pp. 285–296. New York: John Wiley & Sons 1981</td> </tr><tr> <td>[4]</td> <td class="space">Cvetković, D.: Discussing graph theory with a computer II, Theorem suggested by the computer. Publ. Inst. Math. Nouv. Ser.33 (47), 29–33 (1983) · <a href="/0522.05068" class="nowrap">Zbl 0522.05068</a></td> </tr><tr> <td>[5]</td> <td class="space">Cvetković, D.: Further experiences in computer aided research in graph theory. In: Graphs, Hypergraphs and Applications (Proc. Conf. Graph Theory held in Eyba, October 1984) edited by Sachs, H. pp. 27–30. Leipzig: Teubner Verlagsgesselschaft 1985</td> </tr><tr> <td>[6]</td> <td class="space">Cvetković, D., Doob, M.: Developments in the theory of graph spectra. Linear Multilinear Algebra18, 153–181 (1985) · <a href="/0615.05039" class="nowrap">Zbl 0615.05039</a> · <a href="https://doi.org/10.1080/03081088508817683" class="nowrap">doi:10.1080/03081088508817683</a></td> </tr><tr> <td>[7]</td> <td class="space">Cvetković, D., Doob, M., Gutman, I., Torgašev, A.: Recent Results in the Theory of Graph Spectra. North-Holland (to appear) · <a href="/0634.05054" class="nowrap">Zbl 0634.05054</a></td> </tr><tr> <td>[8]</td> <td class="space">Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs–Theory and Application, 2nd edition. Berlin: Deutscher Verlag der Wissenschaften 1982, New York: Academic Press 1982 · <a href="/0824.05046" class="nowrap">Zbl 0824.05046</a></td> </tr><tr> <td>[9]</td> <td class="space">Cvetković, D., Petrić, M.: A table of connected graphs on six vertices. Discrete Math.50, 37–49 (1984) · <a href="/0533.05052" class="nowrap">Zbl 0533.05052</a> · <a href="https://doi.org/10.1016/0012-365X(84)90033-5" class="nowrap">doi:10.1016/0012-365X(84)90033-5</a></td> </tr><tr> <td>[10]</td> <td class="space">Cvetković, D., Radosavljević, Z.: A table of regular graphs with at most 10 vertices. In: Proc. VI Yugoslav Sem. Graph Theory (to appear) · <a href="/0612.05037" class="nowrap">Zbl 0612.05037</a></td> </tr><tr> <td>[11]</td> <td class="space">Hoffman, A.J., Smith, J.H.: On spectral radii of topologically equivalent graphs. In: Recent advances in graph theory, edited by Friedler, M. pp. 273–281. Praha: Academia 1975</td> </tr><tr> <td>[12]</td> <td class="space">Kawasaki, K., Mizutani, K., Hosoya, H.: Tables of non-adjacent numbers, characteristic polynomials and topological indices, II, Mono- and bicyclic graphs. Natur. Sci. Rep. Ochanomizu Univ.22 (2), 181–214 (1971) · <a href="/0247.05138" class="nowrap">Zbl 0247.05138</a></td> </tr><tr> <td>[13]</td> <td class="space">Li, Q., Feng, K.: On the largest eigenvalue of graphs (in Chinese). Acta Math. Appl. Sin.2, 167–175 (1979)</td> </tr><tr> <td>[14]</td> <td class="space">Riordan, J.: An Introduction to Combinatorial Analysis. Princeton: Princeton University Press 1978 · <a href="/0078.00805" class="nowrap">Zbl 0078.00805</a></td> </tr><tr> <td>[15]</td> <td class="space">Schwenk, A.J.: Computing the characteristic polynomial of a graph. In: Graphs and Combinatorics (Lecture Notes in Mathematics 406), edited by Bari, R.A., Harary, F. pp. 153–173. New York: Springer-Verlag 1974</td> </tr><tr> <td>[16]</td> <td class="space">Schwenk, A.J.: Almost all trees are cospectral. In: New directions in the theory of graphs, edited by Harary, F. pp. 275–307. New York-London: Academic Press 1973</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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