Results 51 to 60 of about 412,655 (203)
Edge colouring line graphs of unicyclic graphs
Discrete Applied Mathematics, 1992 A characterization of line graphs of unicyclic graphs is established, and it is proved that the line graph \(G\) of a unicyclic graph is in class 1 unless \(G\) is an odd cycle and an optimal edge colouring of the line graph of a unicyclic graph can be computed in time \(O(| E|)\) (note that the chromatic index problem is known to be \(NP\)-complete ...
Leizhen Cai, John A. Ellis
openaire +2 more sources
On the spectral moments of unicyclic graphs with fixed diameter [PDF]
, 2012 Unicyclic graphs are connected graphs in which the number of edges equals the number of vertices. Let Un,d be the class of unicyclic graphs of order n and diameter d. For unicyclic graphs, lexicographic ordering by spectral moments (S-order) is discussed
Liu, Bolian, Cheng, Bo, Liu, Jianxi
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The Laplacian Spectral Radius of a Class of Unicyclic Graphs
Journal of Applied Mathematics, 2013 Let C(n,k) be the set of all unicyclic graphs with n vertices and cycle length k. For any U∈C(n,k), U consists of the (unique) cycle (say Ck) of length k and a certain number of trees attached to the vertices of Ck having (in total) n-k edges.
Haixia Zhang
doaj +1 more source
The Estrada index of unicyclic graphs [PDF]
, 2012 The Estrada index of a graph G is defined as EE(G)=∑i=1neλi, where λ1,λ2,…,λn are the eigenvalues of G. We determine the unique unicyclic graph with maximum Estrada index, the unique bipartite unicyclic graph with maximum Estrada index, and the unique ...
Du, Zhibin, Zhou, Bo, Bo Zhou, Zhibin Du
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Journal of Applied Mathematics, 2012 Let Φ(G,λ)=det(λIn-L(G))=∑k=0n(-1)kck(G)λn-k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. In this paper, we give four transforms on graphs that decrease all Laplacian coefficients ck(G) and investigate a conjecture A.
Xinying Pai, Sanyang Liu
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Atom-bond connectivity index and diameter of graphs
Journal of Hebei University of Science and Technology, 2016 For further study of the numerous nice properties of topological indices in physical and chemical fields, it is worth considering the relation between a degree-based index and a distance-based index.
Lin WU, Yumei HU
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The Largest Laplacian Spectral Radius of Unicyclic Graphs with Fixed Diameter
Journal of Applied Mathematics, 2013 We identify graphs with the maximal Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d.
Haixia Zhang
doaj +1 more source
Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination
IEEE Access, 2019 Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M1 and the second Zagreb index M2 have already studied. In particular, it has been presented, the first Zagreb index M1 and the second Zagreb index M2 of trees T in ...
Doost Ali Mojdeh +3 more
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Unicyclic graphs with large energy [PDF]
, 2011 We study the energy (i.e., the sum of the absolute values of all eigenvalues) of so-called tadpole graphs, which are obtained by joining a vertex of a cycle to one of the ends of a path.
Stephan Wagner +5 more
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Nearly Hamilton cycles in sublinear expanders and applications
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We develop novel methods for constructing nearly Hamilton cycles in sublinear expanders with good regularity properties, as well as new techniques for finding such expanders in general graphs. These methods are of independent interest due to their potential for various applications to embedding problems in sparse graphs.
Shoham Letzter +2 more
wiley +1 more source