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Lanzhou Index of Trees with Fixed Maximum and Second Maximum Degree
Match Communications in Mathematical and in Computer Chemistry, 2022Summary: Let \(G\) be a finite and simple graph with vertex set \(V(G)\). The Lanzhou index \(G\) is defined as \[ L_z(G) =\sum\limits_{u\in V(G)}d_{\overline{G}}(u)d_G(u)^2; \] where \(d_G(u)\) denotes the degree of vertex \(u\) in \(G\). \textit{N. Dehgardi} and \textit{J.-B. Liu} [MATCH Commun. Math. Comput. Chem. 86, No.
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22017 IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC), 2017
A total k--coloring c of G is called k-neighbor sum distinguishing if for each edge uv, the sum of color of u and the colors of its incident edges is different from the sum of color of v and the colors of its incident edges. The smallest k is called the neighbor sum distinguishing total chromatic number.
Baojian Qiu +3 more
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A total k--coloring c of G is called k-neighbor sum distinguishing if for each edge uv, the sum of color of u and the colors of its incident edges is different from the sum of color of v and the colors of its incident edges. The smallest k is called the neighbor sum distinguishing total chromatic number.
Baojian Qiu +3 more
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Utilitas Mathematica
In this paper, the relations of maximum degree energy and maximum reserve degree energy of a complete graph after removing a vertex have been shown to be proportional to the energy of the complete graph. The results of splitting the graph and shadow graphs are also presented for the complete graph after removing a vertex.
Arooj Ibrahim, Saima Nazeer
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In this paper, the relations of maximum degree energy and maximum reserve degree energy of a complete graph after removing a vertex have been shown to be proportional to the energy of the complete graph. The results of splitting the graph and shadow graphs are also presented for the complete graph after removing a vertex.
Arooj Ibrahim, Saima Nazeer
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Independence, clique size and maximum degree
Combinatorica, 1984Given a graph G with n vertices, maximum degree p, clique size (q-1), and independence number \(\alpha\), the author has previously shown that \(\alpha /n\geq 2/(p+q)\) [Proc. 9th Southeast. Conf. Comb., Graph Theory, Comput., Boca Raton 1978, 269-274 (1978; Zbl 0434.05044)].
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Generalized maximum degree and totally regular graphs
1998A graph \(G\) is \((t,r)\)-regular if the union of the neighborhoods of any set of \(t\) independent vertices has precisely \(r\) vertices. If the graph \(G\) is \((t,r(t))\)-regular for each \(1 \leq t \leq \beta(G)\), then the graph is totally regular, and if \(r(t) = r\) for all \(1 \leq t \leq \beta(G)\), then \(G\) is totally \(r\)-regular.
Haynes, Teresa W., Knisley, Debra
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Maximum Likelihood Degree, Complete Quadrics, and $\mathbb{C}^*$-Action
SIAM Journal on Applied Algebra and Geometry, 2021Mateusz Michałek +2 more
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Reliability computation via a transformed mixed-degree cubature rule and maximum entropy
Applied Mathematical Modelling, 2022Jun Xu
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Enumeration of subtrees and BC-subtrees with maximum degree no more than k in trees
Theoretical Computer Science, 2021Hua Wang, Xiao-dong Zhang
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