Dominator Coloring of Central Graphs

Kavitha, K.; David, N. Gnanamalar

doi:10.5120/8093-1673

Cited by 18 publications

(11 citation statements)

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“…A dominator coloring [ [5], [6], [7], [8], [9]] of a graph is a proper coloring such that each vertex dominates every vertex in at least one color class consisting of vertices with the same color. The chromatic number of a graph G is the minimum number of colors needed in a dominator coloring of G.…”

Section: Definition 2: Dominator Coloringmentioning

confidence: 99%

“…A star K 1,n is a tree with n vertices of degree 1and root vertex has degree n. Definition 5: Wheel Graph [6] A wheel graph is the join of and star graph . Definition 6: Helm Graph [9] The Helm Graph is the graph obtained from a wheel graph by attaching a pendant edge at each vertex of the ncycle. Definition 7: Flower Graph [9] A flower graph is the graph obtained from a helm by joining each pendant vertex to the central vertex of the helm.…”

Section: Definition 4: Star Graphmentioning

confidence: 99%

“…Definition 6: Helm Graph [9] The Helm Graph is the graph obtained from a wheel graph by attaching a pendant edge at each vertex of the ncycle. Definition 7: Flower Graph [9] A flower graph is the graph obtained from a helm by joining each pendant vertex to the central vertex of the helm.…”

Section: Definition 4: Star Graphmentioning

confidence: 99%

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Power Dominator Chromatic Number for some Special Graphs

Maheswari*¹,

J²

2019

IJITEE

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 Abstract: Let G = (V, E) be a finite, connected, undirected with no loops, multiple edges graph. Then the power dominator coloring of G is a proper coloring of G, such that each vertex of G power dominates every vertex of some color class. The minimum number of color classes in a power dominator coloring of the graph, is the power dominator chromatic number . Here we study the power dominator chromatic number for some special graphs such as Bull Graph, Star Graph, Wheel Graph, Helm graph with the help of induction method and Fan Graph. Suitable examples are provided to exemplify the results.

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Section: Definition 2: Dominator Coloringmentioning

confidence: 99%

Section: Definition 4: Star Graphmentioning

confidence: 99%

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Power Dominator Chromatic Number for some Special Graphs

Maheswari*¹,

J²

2019

IJITEE

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“…In this paper, we determine exact values of the nonsplit domination number of central graph and the nonsplit bondage number of central graph for some standard graphs. The following definitions and theorem have been used in the subsequent section and we review the notions in [6] and [7]. Wheel graph is the base graph of Fan graph, Helm graph and Gear graph.…”

Section: Introductionmentioning

confidence: 99%

The nonsplit bondage number of central graph

R.¹,

Y.²

2020

Malaya J. Mat.

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A set D of vertices in a graph G = (V, E) is a nonsplit dominating set if the induced subgraph V − D is connected. The minimum cardinality of a nonsplit dominating set is called the nonsplit domination number of G and is denoted γ ns (G). The nonsplit bondage number of a central graph b ns (C(G)) is the minimum cardinality of a set E of edges for which γ ns (C(G) − E) > γ ns (C(G)). In this paper, we obtain the nonsplit domination number of central graph (γ ns (C(G))) and the bondage number of central graph (b ns (C(G))) are obtained for some standard graphs.

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“…Star networks are one of the common network topologies that are modeled after the star graph which plays an important role in distributed computing. Definition 3.3: A fan graph F n is a graph P n + K 1 which is constructed from a wheel graph W n by deleting one edge in C n [10,11]. A graph is called a friendship graph if every pair of its vertices has exactly one common neighbour.…”

Section: Skew Edge Coloring Of Certain Classes Of Graphsmentioning

confidence: 99%