18,380 research outputs found
Some topological indices and graph properties
In this paper, by using the degree sequences of graphs, we present sufficient conditions for a graph to be Hamiltonian, traceable, Hamilton-connected or -connected in light of numerous topological indices such as the eccentric connectivity index, the eccentric distance sum, the connective eccentricity index
A generalization of Ore's Theorem involving neighborhood unions
AbstractLet G be a graph of order n. Settling conjectures of Chen and Jackson, we prove the following generalization of Ore's Theorem: If G is 2-connected and |N(u)∪N(v)|⩾12n for every pair of nonadjacent vertices u,v, then either G is hamiltonian, or G is the Petersen graph, or G belongs to one of three families of exceptional graphs of connectivity 2
Graphs and Ideals generated by some 2-minors
Let G be a finite graph on [n] = {1,2,3,...,n}, X a 2 times n matrix of
indeterminates over a field K, and S = K[X] a polynomial ring over K. In this
paper, we study about ideals I_G of S generated by 2-minors [i,j] of X which
correspond to edges {i,j} of G. In particular, we construct a Groebner basis of
I_G as a set of paths of G and compute a primary decomposition.Comment: 14 pages, to appear in Communications in Algebr
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