b-Chromatic Sum and b-Continuity Property of Some Graphs
| Autor: | M. S. Sunitha, P. C. Lisna |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Class (set theory)
Computer Networks and Communications Computer Science::Information Retrieval Chromatic sum Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Graph Continuity property Vertex (geometry) Combinatorics TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Computer Science::General Literature ComputingMilieux_MISCELLANEOUS MathematicsofComputing_DISCRETEMATHEMATICS Mathematics |
| Zdroj: | Journal of Interconnection Networks. 21 |
| ISSN: | 1793-6713 0219-2659 |
| DOI: | 10.1142/s0219265921500122 |
| Popis: | A b-coloring of a graph [Formula: see text] is a proper coloring of the vertices of [Formula: see text] such that there exist a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph [Formula: see text], denoted by [Formula: see text], is the largest integer [Formula: see text] such that [Formula: see text] has a b-coloring with [Formula: see text] colors. The b-chromatic sum of a graph [Formula: see text], denoted by [Formula: see text], is introduced and it is defined as the minimum of sum of colors [Formula: see text] of [Formula: see text] for any [Formula: see text] in a b-coloring of [Formula: see text] using [Formula: see text] colors. A graph [Formula: see text] is b-continuous, if it admits a b-coloring with [Formula: see text] colors, for every [Formula: see text]. In this paper, the [Formula: see text]-continuity property of corona of two cycles, corona of two star graphs and corona of two wheel graphs with unequal number of vertices is discussed. The b-continuity property of corona of any two graphs with same number of vertices is also discussed. Also, the b-continuity property of Mycielskian of complete graph, complete bipartite graph and paths are discussed. The b-chromatic sum of power graph of a path is also obtained. |
| Databáze: | OpenAIRE |
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