Some Results on incidence coloring, star arboricity and domination number

Two inequalities bridging the three isolated graph invariants, incidence chromatic number, star arboricity and domination number, were established. Consequently, we deduced an upper bound and a lower bound of the incidence chromatic number for all graphs. Using these bounds, we further reduced the upper bound of the incidence chromatic number of planar graphs and showed that cubic graphs with orders not divisible by four are not 4-incidence colorable. The incidence chromatic numbers of Cartesian product, join and union of graphs were also determined.Comment: 8 page

Full edge-friendly index sets of complete bipartite graphs

‎‎Let $G=(V,E)$ be a simple graph‎. ‎An edge labeling $f:Eto {0,1}$ induces a vertex labeling $f^+:VtoZ_2$ defined by $f^+(v)equiv sumlimits_{uvin E} f(uv)pmod{2}$ for each $v in V$‎, ‎where $Z_2={0,1}$ is the additive group of order 2‎. ‎For $iin{0,1}$‎, ‎let‎ ‎$e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$‎. ‎A labeling $f$ is called edge-friendly if‎ ‎$|e_f(1)-e_f(0)|le 1$‎. ‎$I_f(G)=v_f(1)-v_f(0)$ is called the edge-friendly index of $G$ under an edge-friendly labeling $f$‎. ‎The full edge-friendly index set of a graph $G$ is the set of all possible edge-friendly indices of $G$‎. ‎Full edge-friendly index sets of complete bipartite graphs will be determined‎

FULL EDGE-FRIENDLY INDEX SETS OF COMPLETE BIPARTITE GRAPHS

Abstract. Let G = (V, E) be a simple graph. An edge labeling f : E → {0, 1} induces a vertex labeling f is called the edge-friendly index of G under an edge-friendly labeling f . The full edge-friendly index set of a graph G is the set of all possible edge-friendly indices of G. Full edge-friendly index sets of complete bipartite graphs will be determined

On the Integer-antimagic Spectra of Non-Hamiltonian Graphs

Let $A$ be a nontrivial abelian group. A connected simple graph $G = (V, E)$ is $A$-\textbf{antimagic} if there exists an edge labeling $f: E(G) \to A \setminus \{0\}$ such that the induced vertex labeling $f^+: V(G) \to A$, defined by $f^+(v) = \Sigma$ $\{f(u,v): (u, v) \in E(G) \}$, is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs