Results 51 to 60 of about 532 (122)
Journal of Mathematics, Volume 2025, Issue 1, 2025.The multiplicative sum Zagreb index of a graph G is defined as the product of the sum of the degrees of adjacent vertices of G. A molecular tree is an acyclic connected graph with maximum degree at most 4. A vertex in a molecular tree with degree 3 or 4 is referred to as a branching vertex. In this paper, we consider the class of all molecular trees of
Sadia Noureen +6 more
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A Study on Edge-Set Graphs of Certain Graphs
, 2015 Let $G(V, E)$ be a simple connected graph, with $|E| = \epsilon.$ In this paper, we define an edge-set graph $\mathcal G_G$ constructed from the graph $G$ such that any vertex $v_{s,i}$ of $\mathcal G_G$ corresponds to the $i$-th $s$-element subset of $E(
Chithra, K. P., Kok, Johan, Sudev, N. K.
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The Wiener and Terminal Wiener indices of trees [PDF]
, 2013 Heydari \cite{heydari2013} presented very nice formulae for the Wiener and terminal Wiener indices of generalized Bethe trees. It is pity that there are some errors for the formulae.
Chen, Ya-Hong, Zhang, Xiao-Dong
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A Constructive Extension of the Characterization on Potentially Ks,t-Bigraphic Pairs
Discussiones Mathematicae Graph Theory, 2017 Let Ks,t be the complete bipartite graph with partite sets of size s and t. Let L1 = ([a1, b1], . . . , [am, bm]) and L2 = ([c1, d1], . . . , [cn, dn]) be two sequences of intervals consisting of nonnegative integers with a1 ≥ a2 ≥ . . . ≥ am and c1 ≥ c2
Guo Ji-Yun, Yin Jian-Hua
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Discussiones Mathematicae Graph Theory, 2018 A digraph is called irregular if its distinct vertices have distinct degree pairs. An irregular digraph is called minimal (maximal) if the removal of any arc (addition of any new arc) results in a non-irregular digraph. It is easily seen that the minimum
Górska Joanna +4 more
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On the existence of tripartite graphs and n-partite graphs
Open MathematicsA sequence α\alpha of nonnegative integers is said to be graphic if it is the degree sequence of a simple graph GG, and such a graph GG is called a realization of α\alpha .
Guo Jiyun +4 more
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The Bipartite-Splittance of a Bipartite Graph
Discussiones Mathematicae Graph Theory, 2019 A bipartite-split graph is a bipartite graph whose vertex set can be partitioned into a complete bipartite set and an independent set. The bipartite- splittance of an arbitrary bipartite graph is the minimum number of edges to be added or removed in ...
Yin Jian-Hua, Guan Jing-Xin
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Irreversible 2-conversion set in graphs of bounded degree [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 An irreversible $k$-threshold process (also a $k$-neighbor bootstrap percolation) is a dynamic process on a graph where vertices change color from white to black if they have at least $k$ black neighbors. An irreversible $k$-conversion set of a graph $G$
Jan Kynčl +2 more
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ON ZAGREB INDICES AND ECCENTRIC CONNECTIVITY INDEX OF CERTAIN THORN GRAPHS
, 2016 The first three Zagreb indices of a graph G denoted, M1(G),M2(G) and M3(G), are well known. Equally well known is the eccentricity connectivity index denoted, ξ(G).
U. Mary +4 more
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Brouwer's conjecture for the sum of the k largest Laplacian eigenvalues of some graphs
Open MathematicsLet GG be a graph with n(G)n\left(G) vertices and e(G)e\left(G) edges, and Sk(G){S}_{k}\left(G) be the sum of the kk largest Laplacian eigenvalues of GG. Brouwer conjectured that Sk(G)≤e(G)+k+12{S}_{k}\left(G)\le e\left(G)+\left(\phantom{\rule[-0.75em]{}{
Wang Ke +3 more
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