196 research outputs found
Twin edge coloring of total graph and graphs with twin chromatic index +
A twin edge coloring of a graph G is meant a proper edge coloring of G whose colors come from the integers modulo k that induce a proper vertex coloring in which the color of a vertex is the sum of the colors of its incident edges. The minimum k for which G has a twin edge coloring is the twin chromatic index of G. In this paper, I compute twin chromatic index of total graph of path and cycle also construct some special graphs with twin chromatic index is maximum degree plus two
Group Irregular Labelings of Disconnected Graphs
We investigate the \textit{group irregularity strength} () of graphs, i.e. the smallest value of such that taking any Abelian group \gr of order , there exists a function f:E(G)\rightarrow \gr such that the sums of edge labels at every vertex are distinct. We give the exact values and bounds on for chosen families of disconnected graphs. In addition we present some results for the \textit{modular edge gracefulness} , i.e. the smallest value of such that there exists a function f:E(G)\rightarrow \zet_s such that the sums of edge labels at every vertex are distinct
The integer-antimagic spectra of a disjoint union of Hamiltonian graphs
Let A be a nontrivial abelian group. A simple graph G = (V,E) is A-antimagic, if there exists an edge labeling f: E(G) → A\{0} such that the induced vertex labeling (Formula Presented) is a one-to-one map. The integer-antimagic spectrum of a graph G is the set IAM(G) = {k: G is Zk-antimagic and k ≥ 2}. In this paper, we determine the integer-antimagic spectra for a disjoint union of Hamiltonian graphs
Group-antimagic Labelings of Multi-cyclic Graphs
Let be a non-trivial abelian group. A connected simple graph is -\textbf{antimagic} if there exists an edge labeling such that the induced vertex labeling , defined by , is a one-to-one map. The \textit{integer-antimagic spectrum} of a graph is the set IAM. In this paper, we analyze the integer-antimagic spectra for various classes of multi-cyclic graphs
The Integer-antimagic Spectra of Graphs with a Chord
Let be a nontrival abelian group. A connected simple graph is -antimagic if there exists an edge labeling such that the induced vertex labeling , defined by , is injective. The integer-antimagic spectrum of a graph is the set IAM . In this paper, we determine the integer-antimagic spectra for cycles with a chord, paths with a chord, and wheels with a chord
On the Integer-antimagic Spectra of Non-Hamiltonian Graphs
Let be a nontrivial abelian group. A connected simple graph is -\textbf{antimagic} if there exists an edge labeling such that the induced vertex labeling , defined by , is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs
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