Bounds on the number of complete subgraphs

On the number of complete subgraphs of a graph II

Generalizing some results of P . ERnbs and sonic of L . MosER and J. W. MOON we give lower bounds *on the number of complete p-graphs K p of,graphs in terms of the numbers of vertices and edges. Further, for some values of n and E we give a complete characterization of the extremal graphs, i.e. the graphs S of n vertices and E edges having minimum number of K,'s. Our results contain the proof o...

On the number of complete subgraphs contained in certain graphs

We count the number of complete graphs of order 4 contained in certain graphs.

Bounds on the restrained Roman domination number of a graph

A {em Roman dominating function} on a graph $G$ is a function$f:V(G)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}A {em restrained Roman dominating}function} $f$ is a {color{blue} Roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} The wei...

Lower bounds for the number noncrossing free subgraphs of Kn

Bounds on the outer-independent double Italian domination number

An outer-independent double Italian dominating function (OIDIDF)on a graph $G$ with vertex set $V(G)$ is a function$f:V(G)longrightarrow {0,1,2,3}$ such that if $f(v)in{0,1}$ for a vertex $vin V(G)$ then $sum_{uin N[v]}f(u)geq3$,and the set $ {uin V(G)|f(u)=0}$ is independent. The weight ofan OIDIDF $f$ is the value $w(f)=sum_{vin V(G)}f(v)$. Theminimum weight of an OIDIDF on a graph $G$ is cal...