some lower bounds for the $l$-intersection number of graphs

Some lower bounds for the $L$-intersection number of graphs

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

Some lower bounds for the L-intersection number of graphs

For a set of non-negative integers L, the L-intersection number of a graph is the smallest number l for which there is an assignment of subsets Av ⊆ {1, . . . , l} to vertices v, such that every two vertices u, v are adjacent if and only if |Au ∩ Av| ∈ L. The bipartite L-intersection number is defined similarly when the conditions are considered only for the vertices in different parts. In this...

Some Lower Bounds for Estrada Index

General Lower Bounds for the Minor Crossing Number of Graphs

There are three general lower bound techniques for the crossing numbers of graphs: the Crossing Lemma, the bisection method and the embedding method. In this contribution, we present their adaptations to the minor crossing number. Using the adapted bounds, we improve on the known bounds on the minor crossing number of hypercubes. We also point out relations of the minor crossing number to strin...

On Lower Bounds for the Matching Number of Subcubic Graphs

We give a complete description of the set of triples (α, β, γ) of real numbers with the following property. There exists a constant K such that αn3 + βn2 + γn1 − K is a lower bound for the matching number ν(G) of every connected subcubic graph G, where ni denotes the number of vertices of degree i for each i.

Lower bounds on the signed (total) $k$-domination number

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...