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Areas","{\"openalex\":\"W1527073563\",\"doi\":\"10.37236/29\"}","2026-05-23T07:00:59.213412705","2026-05-23T07:00:59.213413803","doi","10.37236/29","arxivId","openalexId","W1527073563","abstractText","A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics.Several kinds of labelled graph have been called \"signed\" yet are mathematically very different. I distinguish four types:Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon (or along any walk). Among the natural generalizations are larger groups and vertex signs.Sign-colored graphs, in which the edges are labelled from a two-element set that is acted upon by the sign group: - interchanges labels, + leaves them unchanged. This is the kind of \"signed graph\" found in knot theory. The natural generalization is to more colors and more general groups — or no group.Weighted graphs, in which the edge labels are the elements +1 and -1 of the integers or another additive domain. Weights behave like numbers, not signs; thus I regard work on weighted graphs as outside the scope of the bibliography — except (to some extent) when the author calls the weights \"signs\".Labelled graphs where the labels have no structure or properties but are called \"signs\" for any or no reason.","publishedDate","2018-12-21","publishedYear",2018,"venue","The Electronic Journal of Combinatorics",221,"authors","keywords",[169,170,171],"pdfUrl","https://www.combinatorics.org/ojs/index.php/eljc/article/download/DS8/pdf","topVenue",true,"Advanced Graph Theory Research","semigroups and automata theory","Advanced Combinatorial Mathematics","paper_W2055584434","On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs","{\"openalex\":\"W2055584434\",\"doi\":\"10.1090/s0002-9947-1983-0712251-1\"}","2026-05-23T04:34:45.189751088","2026-05-23T04:34:45.189752911","10.1090/s0002-9947-1983-0712251-1","W2055584434","The doubly indexed Whitney numbers of a finite, ranked partially ordered set L L are (the first kind) w i j = ∑ { μ ( x i , x j ) : x i , x j ∈ L {w_{ij}} = \\sum {\\{ \\mu ({x^i},{x^j}):{x^i},{x^j} \\in L} with ranks i , j } i,j\\} and (the second kind) W i j = {W_{ij}} = the number of ( x i , x j ) ({x^i},{x^j}) with x i ⩽ x j {x^i} \\leqslant {x^j} . 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Thomas Zasĺavsky 人物

Thomas Zasĺavsky · 相关论文