26 research outputs found
Complete characterization of s-bridge graphs with local antimagic chromatic number 2
An edge labeling of a connected graph is said to be local
antimagic if it is a bijection such that for any
pair of adjacent vertices and , , where the induced
vertex label , with ranging over all the edges incident
to . The local antimagic chromatic number of , denoted by ,
is the minimum number of distinct induced vertex labels over all local
antimagic labelings of . In this paper, we characterize -bridge graphs
with local antimagic chromatic number 2
Local antimagic chromatic number of partite graphs
Let be a connected graph with and . A bijection
is called a local antimagic labeling of if
for any two adjacent vertices and , , where , and is the set of edges incident to . Thus,
any local antimagic labeling induces a proper vertex coloring of where the
vertex is assigned the color . The local antimagic chromatic number
is the minimum number of colors taken over all colorings induced by local
antimagic labelings of . Let . In this paper, the local antimagic
chromatic number of a complete tripartite graph , and copies of
a complete bipartite graph where are
determined
Local Antimagic Coloring of Some Graphs
Given a graph , a bijection
is called a local antimagic labeling of if the vertex weight is distinct for all adjacent vertices. The vertex
weights under the local antimagic labeling of induce a proper vertex
coloring of a graph . The \textit{local antimagic chromatic number} of
denoted by is the minimum number of weights taken over all such
local antimagic labelings of . In this paper, we investigate the local
antimagic chromatic numbers of the union of some families of graphs, corona
product of graphs, and necklace graph and we construct infinitely many graphs
satisfying