On inverse sum indeg energy of graphs
نویسندگان
چکیده
Abstract For a simple graph with vertex set { v 1 , 2 … n } \left\{{v}_{1},{v}_{2},\ldots ,{v}_{n}\right\} and degree sequence d i = , {d}_{{v}_{i}}\hspace{0.33em}i=1,2,\ldots ,n , the inverse sum indeg matrix (ISI matrix) A ISI ( G ) a j {A}_{{\rm{ISI}}}\left(G)=\left({a}_{ij}) of G is square order n, where + {a}_{ij}=\frac{{d}_{{v}_{i}}{d}_{{v}_{j}}}{{d}_{{v}_{i}}+{d}_{{v}_{j}}}, if {v}_{i} adjacent to {v}_{j} 0, otherwise. The multiset eigenvalues τ ≥ form="prefix">≥ ⋯ {\tau }_{1}\ge }_{2}\hspace{0.33em}\ge \cdots \ge }_{n} {A}_{{\rm{ISI}}}\left(G) known as ISI spectrum . energy ∑ ∣ \mathop{\sum }\limits_{i=1}^{n}| }_{i}| absolute . G. In this article, we give some properties graphs. Also, obtain bounds characterize extremal Furthermore, construct pairs equienergetic graphs for each 9 n\ge 9
منابع مشابه
Some remarks on the sum of the inverse values of the normalized signless Laplacian eigenvalues of graphs
Let G=(V,E), $V={v_1,v_2,ldots,v_n}$, be a simple connected graph with $%n$ vertices, $m$ edges and a sequence of vertex degrees $d_1geqd_2geqcdotsgeq d_n>0$, $d_i=d(v_i)$. Let ${A}=(a_{ij})_{ntimes n}$ and ${%D}=mathrm{diag }(d_1,d_2,ldots , d_n)$ be the adjacency and the diagonaldegree matrix of $G$, respectively. Denote by ${mathcal{L}^+}(G)={D}^{-1/2}(D+A) {D}^{-1/2}$ the normalized signles...
متن کاملOn the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs
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...
متن کاملSuper Pair Sum Labeling of Graphs
Let $G$ be a graph with $p$ vertices and $q$ edges. The graph $G$ is said to be a super pair sum labeling if there exists a bijection $f$ from $V(G)cup E(G)$ to ${0, pm 1, pm2, dots, pm (frac{p+q-1}{2})}$ when $p+q$ is odd and from $V(G)cup E(G)$ to ${pm 1, pm 2, dots, pm (frac{p+q}{2})}$ when $p+q$ is even such that $f(uv)=f(u)+f(v).$ A graph that admits a super pair sum labeling is called a {...
متن کاملGraphs with Constant Sum of Domination and Inverse Domination Numbers
A subsetD of the vertex set of a graph G, is a dominating set if every vertex in V −D is adjacent to at least one vertex inD. The domination number γ G is the minimum cardinality of a dominating set of G. A subset of V −D, which is also a dominating set of G is called an inverse dominating set of G with respect toD. The inverse domination number γ ′ G is the minimum cardinality of the inverse d...
متن کاملOn the energy of non-commuting graphs
For given non-abelian group G, the non-commuting (NC)-graph $Gamma(G)$ is a graph with the vertex set $G$ $Z(G)$ and two distinct vertices $x, yin V(Gamma)$ are adjacent whenever $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Special Matrices
سال: 2023
ISSN: ['2300-7451']
DOI: https://doi.org/10.1515/spma-2022-0175