Max flow vitality in general and st‐planar graphs
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DOI: 10.1002/net.21878
Abstract: The vitality of an arc/node of a graph with respect to the maximum flow between two fixed nodes s and t is defined as the reduction of the maximum flow caused by the removal of… read more here.
Keywords: vitality; planar graphs; max flow; vitality arcs ... See more keywords
On (p, 1)-total labelling of planar graphs
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DOI: 10.1007/s10878-015-9958-7
Abstract: A k-(p, 1)-total labelling of a graph G is a function f from $$V(G)\cup E(G)$$V(G)∪E(G) to the color set $$\{0, 1, \ldots , k\}$${0,1,…,k} such that $$|f(u)-f(v)|\ge 1$$|f(u)-f(v)|≥1 if $$uv\in E(G), |f(e_1)-f(e_2)|\ge 1$$uv∈E(G),|f(e1)-f(e2)|≥1 if $$e_1$$e1 and… read more here.
Keywords: labelling; total labelling; labelling planar; planar graphs ... See more keywords
List 2-distance $$\varDelta +3$$Δ+3-coloring of planar graphs without 4,5-cycles
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Combinatorial Optimization"
DOI: 10.1007/s10878-018-0312-8
Abstract: Let $$\chi _2(G)$$χ2(G) and $$\chi _2^l(G)$$χ2l(G) be the 2-distance chromatic number and list 2-distance chromatic number of a graph G, respectively. Wegner conjectured that for each planar graph G with maximum degree $$\varDelta $$Δ at… read more here.
Keywords: distance; list distance; without cycles; vardelta ... See more keywords
On Chromatic Numbers of Two Extensions of Planar Graphs
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DOI: 10.1007/s40306-018-0252-5
Abstract: In this paper, the acyclic chromatic and the circular list chromatic numbers of a simple H-minor free graph G is considered, where H ∈{K5,K3,3}. It is proved that the acyclic chromatic number (resp. the circular… read more here.
Keywords: minor free; number; chromatic number; numbers two ... See more keywords
Differential algebra of cubic planar graphs
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DOI: 10.1016/j.aim.2018.09.002
Abstract: In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In… read more here.
Keywords: algebra cubic; cubic planar; differential algebra; planar graphs ... See more keywords
Investigating the Short-Circuit Problem Using the Planarity Index of Complex q-Rung Orthopair Fuzzy Planar Graphs
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DOI: 10.1155/2021/8295997
Abstract: Planar graphs play an effective role in many practical applications where the crossing of edges becomes problematic. This paper aims to investigate the complex q-rung orthopair fuzzy (CQROF) planar graphs (CQROFPGs). In a CQROFPG, the… read more here.
Keywords: complex qrof; complex rung; planar graphs; qrof ... See more keywords
Independent Bondage Number in Planar Graphs Under Girth Constraints
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DOI: 10.3390/math13223662
Abstract: Given a finite, simple, connected graph G with at least one edge, the independent bondage number bi(G) of G is the minimum size of an edge set, such that its deletion results in a graph… read more here.
Keywords: girth constraints; number; planar graphs; independent bondage ... See more keywords
Star Chromatic Index of 1-Planar Graphs
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DOI: 10.3390/sym14061177
Abstract: Many symmetric properties are well-explored in graph theory, especially in graph coloring, such as symmetric graphs defined by the automorphism groups, symmetric drawing of planar graphs, and symmetric functions which are used to count the… read more here.
Keywords: planar graphs; planar; chromatic index; star chromatic ... See more keywords
The Surviving Rate of IC-Planar Graphs
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DOI: 10.3390/sym14061258
Abstract: Let k and n be two positive integers. Firefighting is a discrete dynamical process of preventing the spread of fire. Let G be a connected graph G with n vertices. Assuming a fire starts at… read more here.
Keywords: surviving rate; planar graphs; rate planar; fire ... See more keywords
Planar Graphs Without 4-Cycles Are (6, 6)-Colorable
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DOI: 10.3390/sym17111865
Abstract: It has been shown that there is a planar graph without 3-cycles which is not (Δ1,Δ2)-colorable for any given Δ1,Δ2. This inspires many research to obtain sufficient conditions for planar graphs without 4-cycles and other… read more here.
Keywords: graphs without; planar graphs; cycles colorable; without cycles ... See more keywords