Results 21 to 30 of about 963 (204)
On 2-power unicyclic cubic graphs
Electronic Journal of Graph Theory and Applications, 2022 In a graph, a cycle whose length is a power of two (that is, 2k) is called a 2-power cycle. In this paper, we show that the existence of an infinite family of cubic graphs which contain only one cycle whose length is a power of 2.
Shariefuddin Pirzada +2 more
doaj +3 more sources
Edge colouring line graphs of unicyclic graphs
Discrete Applied Mathematics, 1992 The chromatic index problem is known to be NP-complete, even for line graphs. In this paper we show that the chromatic index of the line graph of a unicyclic graph is equal to its maximum degree unless it is an odd cycle.
Cai, Leizhen, Ellis, John A.
core +2 more sources
Burning Numbers of t-unicyclic Graphs [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 Given a graph $G$, the burning number of $G$ is the smallest integer $k$ for which there are vertices $x_1, x_2,\ldots,x_k$ such that $(x_1,x_2,\ldots,x_k)$ is a burning sequence of $G$. It has been shown that the graph burning problem is NP-complete, even for trees with maximum degree three, or linear forests. A $t$-unicyclic graph is a unicycle graph
Ruiting Zhang, Yingying Yu, Huiqing Liu
openaire +3 more sources
UNICYCLIC GRAPHS WITH EQUAL LAPLACIAN ENERGY [PDF]
Linear and Multilinear Algebra, 2013 We introduce a new operation on a class of graphs with the property that the Laplacian eigenvalues of the input and output graphs are related. Based on this operation, we obtain a family of Θ( n) noncospectral unicyclic graphs on n vertices with the same
Eliseu Fritscher +2 more
core +3 more sources
Unicyclic components in random graphs [PDF]
Journal of Physics A: Mathematical and General, 2004 4 pages, 2 ...
E. Ben-Naim, Paul L. Krapivsky
openaire +2 more sources
High-ordered spectral characterization of unicyclic graphs
, 2022 In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let $G$ be a graph and $G^m$ be the $m$-th power (hypergraph) of $G$.
Fan, Yi-Zheng +2 more
core +2 more sources
The Signless Laplacian Estrada Index of Unicyclic Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 For a simple graph G, the signless Laplacian Estrada index is defined as SLEE(G)=∑ni=1eqi, where q1, q2,..., qn are the eigenvalues of the signless Laplacian matrix of G.
Hamid Reza Ellahi +3 more
doaj +1 more source
Binomial edge ideals of unicyclic graphs [PDF]
International Journal of Algebra and Computation, 2021 Let [Formula: see text] be a connected graph on the vertex set [Formula: see text]. Then [Formula: see text]. In this paper, we prove that if [Formula: see text] is a unicyclic graph, then the depth of [Formula: see text] is bounded below by [Formula: see text]. Also, we characterize [Formula: see text] with [Formula: see text] and [Formula: see text].
openaire +2 more sources
The inverse of the incidence matrix of a unicyclic graph [PDF]
Linear and Multilinear Algebra, 2022 The vertex-edge incidence matrix of a (connected) unicyclic graph G is a square matrix which is invertible if and only if the cycle of G is an odd cycle. A combinatorial formula of the inverse of the incidence matrix of an odd unicyclic graph was known.
Hessert, Ryan, Mallik, Sudipta
openaire +2 more sources
Minor-obstructions for apex sub-unicyclic graphs
, 2020 A graph is sub-unicyclic if it contains at most one cycle. A graph G is k-apex sub-unicyclic if it can become sub-unicyclic by removing k of its vertices.
Singh, A. +5 more
core +2 more sources