Results 41 to 50 of about 167 (98)
A Study on Variants of Status Unequal Coloring in Graphs and Its Properties
Journal of Mathematics, Volume 2024, Issue 1, 2024.Let G∧ be a simple connected graph with vertex set ϑG∧ and edge set ξG∧. The status of a vertex p∈ϑG∧ is defined as ∑q≠pd(p, q). A subset P of ϑG∧ is called a status unequal dominating set (stu‐dominating set) of G∧; for every q∈ϑ−P, there exists p in P such that p and q are adjacent and st(p) ≠ st(q).
Parvathy Gnana Sambandam +4 more
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Independence Number, Connectivity and All Fractional (a, b, k)-Critical Graphs
Discussiones Mathematicae Graph Theory, 2019 Let G be a graph and a, b and k be nonnegative integers with 1 ≤ a ≤ b. A graph G is defined as all fractional (a, b, k)-critical if after deleting any k vertices of G, the remaining graph has all fractional [a, b]-factors.
Yuan Yuan, Hao Rong-Xia
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On the Isometric Path Partition Problem
Discussiones Mathematicae Graph Theory, 2021 The isometric path cover (partition) problem of a graph consists of finding a minimum set of isometric paths which cover (partition) the vertex set of the graph.
Manuel Paul
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Gregarious Kite Factorization of Tensor Product of Complete Graphs
Discussiones Mathematicae Graph Theory, 2020 A kite factorization of a multipartite graph is said to be gregarious if every kite in the factorization has all its vertices in different partite sets. In this paper, we show that there exists a gregarious kite factorization of Km × Kn if and only if mn
Tamil Elakkiya A., Muthusamy A.
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Arbitrarily Partitionable {2K2, C4}-Free Graphs
Discussiones Mathematicae Graph Theory, 2022 A graph G = (V, E) of order n is said to be arbitrarily partitionable if for each sequence λ = (λ1, λ2, …, λp) of positive integers with λ1 +·…·+λp = n, there exists a partition (V1, V2, …, Vp) of the vertex set V such that Vi induces a connected ...
Liu Fengxia +2 more
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Strong Tutte Type Conditions and Factors of Graphs
Discussiones Mathematicae Graph Theory, 2020 Let odd(G) denote the number of odd components of a graph G and k ≥ 2 be an integer. We give sufficient conditions using odd(G − S) for a graph G to have an even factor.
Yan Zheng, Kano Mikio
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The Spectrum Problem for the Connected Cubic Graphs of Order 10
Discussiones Mathematicae Graph Theory, 2021 We show that if G is a connected cubic graph of order 10, then there exists a G-decomposition of Kv if and only if v ≣ 1 or 10 (mod 15) except when v = 10 and G is one of 5 specific graphs.
Adams Peter +3 more
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On Edge H-Irregularity Strengths of Some Graphs
Discussiones Mathematicae Graph Theory, 2021 For a graph G an edge-covering of G is a family of subgraphs H1, H2, . . . , Ht such that each edge of E(G) belongs to at least one of the subgraphs Hi, i = 1, 2, . . . , t. In this case we say that G admits an (H1, H2, . . . , Ht)-(edge) covering.
Naeem Muhammad +4 more
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The Minimum Size of a Graph with Given Tree Connectivity
Discussiones Mathematicae Graph Theory, 2021 For a graph G = (V, E) and a set S ⊆ V of at least two vertices, an S-tree is a such subgraph T of G that is a tree with S ⊆ V (T). Two S-trees T1 and T2 are said to be internally disjoint if E(T1) ∩ E(T2) = ∅ and V (T1) ∩ V (T2) = S, and edge-disjoint ...
Sun Yuefang, Sheng Bin, Jin Zemin
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Sharp Upper Bounds on the Clar Number of Fullerene Graphs
Discussiones Mathematicae Graph Theory, 2018 The Clar number of a fullerene graph with n vertices is bounded above by ⌊n/6⌋ − 2 and this bound has been improved to ⌊n/6⌋ − 3 when n is congruent to 2 modulo 6.
Gao Yang, Zhang Heping
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