A graph $G$ is Ramsey for a $H$ if every colouring of the edges in two colours contains monochromatic copy $H$. Two graphs $H_1$ and $H_2$ are equivalent any only it $H_2$. parameter $s$ distinguishing $s(H_1)\neq s(H_2)$ implies that not equivalent. In this paper we show chromatic number parameter. We also extend to multi-colour case use similar idea find another which distinguishing.

We study the hat chromatic number of a graph defined in following way: there is one player at each vertex G , an adversary places K colors on head player, two players can see other's hats if and only they are adjacent vertices. All simultaneously try to guess color their hat. The cannot communicate but collectively determine strategy before placed. number, denoted by HG ( ) largest such that ab...

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

A generalization of the chromatic number of a graph is introduced such that the colors are integers modulo n, and the colors on adjacent vertices are required to be as far apart as possible.

‎Let $f$ be a proper $k$-coloring of a connected graph $G$ and‎ ‎$Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into‎ ‎the resulting color classes‎. ‎For a vertex $v$ of $G$‎, ‎the color‎ ‎code of $v$ with respect to $Pi$ is defined to be the ordered‎ ‎$k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$‎, ‎where $d(v,V_i)=min{d(v,x):~xin V_i}‎, ‎1leq ileq k$‎. ‎If‎ ‎distinct...