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- Title
Vertex neighborhood restricted edge achromatic sums of graphs.
- Authors
Joseph, Anu; Dominic, Charles
- Abstract
The vertex induced 2-edge coloring number ψ vi 2 ′ (G) of a graph G is the highest number of colors that can occur in an edge coloring of a graph G such that not more than two colors can be used to color the edges in the induced subgraph 〈 N [ v ] 〉 generated by the closed neighborhood N [ v ] of a vertex v in V (G). The vertex induced 2-edge coloring sum of a graph G denoted as ∑ vi 2 ′ (G) , is the greatest sum among all the vertex induced 2-edge coloring of a graph G which concedes ψ vi 2 ′ (G) colors. The vertex incident 2-edge coloring number of a graph G is the highest number of colors required to color the edges of a graph G such that not more than two colors can be ceded to the edges incident at the vertex v of G. The vertex incident 2-edge coloring sum of a graph G denoted as ∑ vi 2 ′ (G) , is the maximum sum among all the vertex incident 2-edge coloring of graph G which receives maximum ψ vin 2 ′ (G) colors. In this paper, we initiate a study on the vertex induced 2-edge coloring sum and vertex incident 2-edge coloring sum concepts and apply the same to some graph classes. Besides finding the exact values of these parameters, we also obtain some bounds and a few comparative results.
- Subjects
GRAPH coloring; COLORS
- Publication
Discrete Mathematics, Algorithms & Applications, 2023, Vol 15, Issue 8, p1
- ISSN
1793-8309
- Publication type
Article
- DOI
10.1142/S1793830922501695