Results 91 to 100 of about 891,390 (207)
Unicyclic graphs with bicyclic inverses [PDF]
Czechoslovak Mathematical Journal, 2017 A graph is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is a graph whose adjacency matrix is similar to A(G)−1 via a particular type of similarity. Let H denote the class of connected bipartite graphs with unique perfect matchings.
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Brooks' theorem with forbidden colors
Journal of Graph Theory, Volume 105, Issue 3, Page 373-385, March 2024.Abstract We consider extensions of Brooks' classic theorem on vertex coloring where some colors cannot be used on certain vertices. In particular we prove that if G $G$ is a connected graph with maximum degree Δ(G)≥4 ${\rm{\Delta }}(G)\ge 4$ that is not a complete graph and P⊆V(G) $P\subseteq V(G)$ is a set of vertices where either (i) at most Δ(G)−2 ${
Carl Johan Casselgren
wiley +1 more source
Journal of Mathematics, Volume 2024, Issue 1, 2024.Nanostar dendrimers are tree‐like nanostructures with a well‐defined, symmetrical architecture. They are built in a step‐by‐step, controlled synthesis process, with each layer or generation building on the previous one. Dendrimers are made up of a central core, a series of repeating units or branches, and a surface group shell.
Syed Ahtsham Ul Haq Bokhary +7 more
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A note on the minimum reduced reciprocal Randic index of n-vertex unicyclic graphs
Kuwait Journal of Science, 2017 Recent studies show that the reduced reciprocal Randi? (RRR) index possesses the second-best correlating ability amongthe several well known topological indices.
Akbar Ali, Akhlaq A. Bhatti
doaj
Graphs with 3-rainbow index $n-1$ and $n-2$ [PDF]
, 2013 Let $G$ be a nontrivial connected graph with an edge-coloring $c:E(G)\rightarrow \{1,2,\ldots,q\},$ $q\in \mathbb{N}$, where adjacent edges may be colored the same. A tree $T$ in $G$ is a $rainbow tree$ if no two edges of $T$ receive the same color.
Li, Xueliang, Yang, Kang, Zhao, Yan
core
Degree distance of unicyclic graphs
Filomat, 2010 The degree distance of a connected graph G with vertex set V(G) is defined as D'(G)= ?u?V (G) dG (u)DG (u), where dG (u) denotes the degree of vertex u and DG (u) denotes the sum of distances between u and all vertices of G. We determine the maximum degree distance of n-vertex unicyclic graphs with given maximum degree, and the first seven maximum ...
Zhibin Du, Bo Zhou
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Locating eigenvalues of unicyclic graphs
Applicable Analysis and Discrete Mathematics, 2017 We present a linear time algorithm that computes the number of eigenvalues of a unicyclic graph in a given real interval. It operates directly on the graph, so that the matrix is not needed explicitly. The algorithm is applied to study the multiplicities of eigenvalues of closed caterpillars, obtain the spectrum of balanced closed ...
Braga, Rodrigo O. +2 more
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The Entropy of Weighted Graphs with Atomic Bond Connectivity Edge Weights
Discrete Dynamics in Nature and Society, 2018 The aim of this report to solve the open problem suggested by Chen et al. We study the graph entropy with ABC edge weights and present bounds of it for connected graphs, regular graphs, complete bipartite graphs, chemical graphs, tree, unicyclic graphs ...
Young Chel Kwun +4 more
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Decomposition of complete graphs into connected bipartite unicyclic graphs with eight edges
Electronic Journal of Graph Theory and Applications, 2019 We prove that each of the 34 non-isomorphic connected unicyclic bipartite graphs with eight edges decomposes the complete graph Kn whenever the necesary conditions are satisfied.
John Fahnenstiel, Dalibor Froncek
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Complement of the generalized total graph of fields
AKCE International Journal of Graphs and Combinatorics, 2020 Let R be a commutative ring and H be a multiplicative prime subset of R. The generalized total graph is the undirected simple graph with vertex set R and two distinct vertices x and y are adjacent if For a field F, is the only multiplicative prime subset
T. Tamizh Chelvam, M. Balamurugan
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