Results 51 to 60 of about 580,793 (206)
Unicyclic graphs with equal Laplacian energy [PDF]
Linear and Multilinear Algebra, 2013 11 pages, 11 figures, slightly modified version of Theorem 1 when compared with original ...
Eliseu Fritscher +2 more
openaire +3 more sources
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
doaj +1 more source
On 2-power unicyclic cubic graphs
Electronic Journal of Graph Theory and Applications, 2022 Summary: In a graph, a cycle whose length is a power of two (that is, \(2^k\)) 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. Such graphs are called as 2-power unicyclic cubic graphs. Further we observe that the only 2-power cycle in a
Shariefuddin Pirzada +2 more
openaire +4 more sources
On the nullity of the line graph of unicyclic graph with depth one [PDF]
, 2012 A connected graph with a unique cycle is called a unicyclic graph. A unicyclic graph with depth one may be thought of as being obtained from a cycle by appending ni pendent edges on each vertex vi in the cycle Ct (for some integer t⩾3), denoted by Cn1,n2,
Fan, Yi-Zheng, Li, Hong-Hai, Su, Li
core +1 more source
Laplacian Spectral Characterization of Some Unicyclic Graphs
Journal of Applied Mathematics, 2014 Let W(n;q,m1,m2) be the unicyclic graph with n vertices obtained by attaching two paths of lengths m1 and m2 at two adjacent vertices of cycle Cq. Let U(n;q,m1,m2,…,ms) be the unicyclic graph with n vertices obtained by attaching s paths of lengths m1,m2,
Lijun Yu, Hui Wang, Jiang Zhou
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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
Sharp Lower Bounds of the Sum-Connectivity Index of Unicyclic Graphs
Journal of Mathematics, 2021 The sum-connectivity index of a graph G is defined as the sum of weights 1/du+dv over all edges uv of G, where du and dv are the degrees of the vertices u and v in graph G, respectively.
Maryam Atapour
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New Sharp Extremal Bounds for the Randić Index of Trees With Prescribed Roman Domination Number
Discrete Dynamics in Nature and Society, Volume 2026, Issue 1, 2026.The Randić index is a classical degree‐based topological index that captures branching features of a graph and has broad applications in chemical graph theory and related network models. Roman domination is a defense‐inspired covering concept in which vertices are assigned protective labels so that every unprotected vertex is adjacent to a strongly ...
Waqar Ali +4 more
wiley +1 more source
A fast practical algorithm for the vertex separation of unicyclic graphs [PDF]
, 2008 The vertex separation of a graph is the minimum vertex separation of a linear layout of that graph over all its linear layouts. A linear layout of a graph is an arrangement of its vertices in a line and the vertex separation of a linear layout is maximum
Markov, Minko Marinov.
core
Trees With a Given Independence Number Maximizing the Randić Index
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.The Randić index is a classical degree‐based descriptor with strong empirical connections to branching‐sensitive physicochemical properties of chemical compounds. Defined as R(G) = ∑uv ∈ E(G)1/√(d(u)d(v)), for a simple connected graph G, this index has been extensively studied, especially in the context of trees.
Bojana Borovićanin +3 more
wiley +1 more source