{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T09:32:00Z","timestamp":1781775120056,"version":"3.54.5"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a connected graph of order $n$. The resistance matrix of $G$ is defined as $R_G=(r_{ij}(G))_{n\\times n}$, where $r_{ij}(G)$ is the resistance distance between two vertices $i$ and $j$ in $G$. Eigenvalues of $R_G$ are called R-eigenvalues of $G$. If all row sums of $R_G$ are equal, then $G$ is called resistance-regular. For any connected graph $G$, we show that $R_G$ determines the structure of $G$ up to isomorphism. Moreover, the structure of $G$ or the number of spanning trees of $G$ is determined by partial entries of $R_G$ under certain conditions. We give some characterizations of resistance-regular graphs and graphs with few distinct R-eigenvalues. For a connected regular graph $G$ with diameter at least $2$, we show that $G$ is strongly regular if and only if there exist $c_1,c_2$ such that $r_{ij}(G)=c_1$ for any adjacent vertices $i,j\\in V(G)$, and $r_{ij}(G)=c_2$ for any non-adjacent vertices $i,j\\in V(G)$.<\/jats:p>","DOI":"10.37236\/5295","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:44:58Z","timestamp":1578692698000},"source":"Crossref","is-referenced-by-count":18,"title":["On the Resistance Matrix of a Graph"],"prefix":"10.37236","volume":"23","author":[{"given":"Jiang","family":"Zhou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhongyu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changjiang","family":"Bu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2016,3,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p41\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p41\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:31:35Z","timestamp":1579239095000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p41"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,4]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5295","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,4]]},"article-number":"P1.41"}}