Hamiltonian claw-free graphs involving minimum degrees

In this paper, by establishing a new graph ?(G) over the semi-direct product of groups, we will first state and prove some graph-theoretical properties, namely, diameter, maximum and minimum degrees, girth, degree sequence, domination number, chromatic number, clique number of ?(G). In the final section we will show that ?(G) is actually a perfect graph.

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Random Planar Graphs with Bounds on the Maximum and Minimum Degrees

Graphs and Combinatorics ◽

10.1007/s00373-010-0960-7 ◽

2010 ◽

Vol 27 (1) ◽

pp. 87-107

Author(s):

Chris Dowden

Keyword(s):

Planar Graphs ◽

Minimum Degrees

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2-Factors of Bipartite Graphs with Asymmetric Minimum Degrees

SIAM Journal on Discrete Mathematics ◽

10.1137/080739513 ◽

2010 ◽

Vol 24 (2) ◽

pp. 486-504 ◽

Cited By ~ 2

Author(s):

Andrzej Czygrinow ◽

Louis DeBiasio ◽

H. A. Kierstead

Keyword(s):

Bipartite Graphs ◽

Minimum Degrees

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Graph Indices for Cartesian Product of F-sum of Connected Graphs

Combinatorial Chemistry & High Throughput Screening ◽

10.2174/1386207324666210217143114 ◽

2021 ◽

Vol 24 ◽

Author(s):

Jia-Bao Liu ◽

Muhammad Imran ◽

Shakila Baby ◽

Hafiz Muhammad Afzal Siddiqui ◽

Muhammad Kashif Shafiq

Keyword(s):

Computer Science ◽

Topological Index ◽

Cartesian Product ◽

Chemical Properties ◽

Physical And Chemical Properties ◽

Finite Graphs ◽

Zagreb Indices ◽

Physical And Chemical ◽

Minimum Degrees ◽

And Chemical Properties

Background: A topological index is a real number associated to a graph, that provides information about its physical and chemical properties along with their correlations.Topological indices are being used successfully in Chemistry, Computer Science and many other fields. Aim and Objective: In this article, we apply the well known, Cartesian product on F-sums of connected and finite graphs. We formulate sharp limits for some famous degree dependent indies. Results: Zagreb indices for the graph operations T(G), Q(G), S(G), R(G) and their F-sums have been computed. By using orders and sizes of component graphs, we derive bounds for Zagreb indices, F-index and Narumi-Katayana index. Conclusion: The formulation of expressions for the complicated products on F-sums, in terms of simple parameters like maximum and minimum degrees of basic graphs, reduces the computational complexities.

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