A metric graph is a pair (G, d), where G and $$d:E(G) \rightarrow \mathbb {R}_{\ge 0}$$ distance function. Let $$p \in [1,\infty ]$$ be fixed. An isometric embedding of the d) in $$\ell _p^k = (\mathbb {R}^k, d_p)$$ map $$\phi :V(G) {R}^k$$ such that $$d_p(\phi (v), \phi (w)) d(vw)$$ for all edges $$vw\in E(G)$$ . The _p$$ -dimension least integer k there exists an _p^k$$ functions d has _p^K$$...

Based on the Hugenholtz–Van Hove theorem, six basic quantities of EoS in isospin asymmetric nuclear matter are expressed terms nucleon kinetic energy t(k), symmetric and parts single-nucleon potentials $$U_0(\rho ,k)$$ $$U_{\text {sym},i}(\rho . The include quadratic symmetry $$E_{\text {sym,2}}(\rho )$$ , quartic {sym,4}}(\rho their corresponding density slopes $$L_2(\rho $$L_4(\rho incompress...

We introduce the class of outerspatial 2-complexes as natural generalisation outerplanar graphs to three dimensions. Answering a question O-joung Kwon, we prove that locally 2-connected 2-complex is if and only it does not contain surface positive genus subcomplex have space minor generalised cone over $K_4$ or $K_{2,3}$.
 This applied nested plane embeddings graphs; is, constrained by con...

The Ramsey number R(G1, G2, G3) is the smallest positive integer n such that for all 3-colorings of the edges of Kn there is a monochromatic G1 in the first color, G2 in the second color, or G3 in the third color. We study the bounds on various 3-color Ramsey numbers R(G1, G2, G3), where Gi ∈ {K3,K3 + e,K4 − e,K4}. The minimal and maximal combinations of Gi’s correspond to the classical Ramsey ...